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Re: is mathematics a religion?

Posted: Tue Aug 05, 2014 4:15 pm UTC
by schapel
I think the main conceptual problem with the thesis of the thread is the idea that mathematics describes the physical world. Actually, math is completely divorced from the physical world. It's an idealized, abstract, formal system. When one uses math in the real world, one models certain aspects of the real world as mathematical objects. But this is just a model, and is not to be confused with the real world. In other words, the map is not the territory. Do not confuse the model, which is a simplified and idealized representation of the real world, with the real world itself.
http://en.wikipedia.org/wiki/Map%E2%80% ... y_relation

Re: is mathematics a religion?

Posted: Tue Aug 05, 2014 4:41 pm UTC
by Gwydion
55555, there are a few issues with your post, and I'm not the best qualified person here to tackle all of them, but I will address a few. First of all, expressions like the ones you're using are "true" but sorta meaningless. The word "infinity" gets thrown around like a number frequently, but doesn't behave like any of the numbers you're used to. Let me translate your opening into words, and see if it still makes sense:

"Imagine the biggest number you can imagine. Like, bigger than anything. If you can imagine a bigger number than that, then your first number wasn't big enough. Keep going. Ok, so you have this biggest number. Now add one to it. What do you get?"

You can hopefully see that this is meaningless - if there was such a thing as a "biggest number", you shouldn't be able to add 1 to it, or else maybe the number should have been bigger in the first place. Trying to add 1 to the "biggest number" is meaningless, so we say that inf + 1 = inf. Mathematicians use this shorthand not in the usual way (so subtracting infinity from both sides doesn't help), but to express that on the scale of infinity, the number one is so small it doesn't do anything significant. Most of your expressions follow from this, as you said (though it was jarring when you started to add more letters without defining them). And at the end, you are correct in saying that inf + inf = inf as well. (I think 10^inf > inf though.)

The other big issue is that you try to reduce this to "everything is infinity and there isn't anything else". You started with the assumption that a "least thing" exists, and called it 1. By concluding this isn't true, you've defined an inconsistent system - either by "proving" one of your assumptions false, or by assuming a statement as well as its negation (which is what you did in the end). From this, you can conclude anything you want, but it doesn't make your ideas any more reasonable, it just shows that your foundations are poor.

Re: is mathematics a religion?

Posted: Wed Aug 06, 2014 1:45 am UTC
by Moole
55555 wrote:I drifted from forum to forum so I am qualified to
say what I am talking now.


Having been poorly received numerous times doesn't exactly count as qualification.

I know that the people who sing at those places say that infinity is the largest possible
amount because if you add 1 to infinity it does not increase: = + 1, therefore the answer to the question is
Z + Y = , X=, and this is possible only if the largest amount Z is equal to infinity.


The question was ill-defined if we allow that as an answer! Infinity is, most certainly not a number. It is much like "multiplication" or "addition" in that it is defined different ways in different fields. Commonly, we might talk about infinite cardinals - that being the size of a set. For instance, we may argue that the set of real numbers is larger than the set of integers, though they are both infinite (see: Cantor's Diagonal Argument). The idea of cardinality is used on sets that have no structure beyond having some elements. If we were talking about the "amount" of things, it would be reasonable to talk about sets with no structure beyond being sets. But we have a problem: we may argue that there is no biggest set, because each the set of subsets of a given set (the power set) is always bigger*. True, adding a new element to the set would not increase its size (see: Hilbert's hotel), nor would doubling the set's size, but the analog of exponentiation would increase size.

The sort of infinity that would be applicable here is more of the topological sense (which is where one would see the symbol ∞ the most- set theorists like their crazy aleph symbols); we can define ∞ and -∞ as, basically, endpoints on the real line** - that is, we could define 2-∞=0 as the limit of 2x as x decreases towards -∞ (which we can say instead of "decreases without bound" because we can define terms like "as x goes to y" such that it makes sense to make y infinite). Indeed, everything here follows if we take all operations to be continuous*** (that is "small variations" in the input cause "small variations" in the output. Loosely speaking) - since x+1 increases without bound when x does, ∞+1 is ∞. This is a well-defined concept and the equations you write do follow under this definition (if C is positive and Y is not -∞).

You can note that I'm using a lot of asterisks. This is because math hates it when everything works out elegantly for the mathematicians or when there is an obvious all-purpose way to extend common concepts to infinities.

This seems to be rather a good song, there are no largest anything, there is no least anything, there is no big there is no small, no hot no cold, no right no wrong, no slow no fast, no abundance no poverty, no left no right, all that we got is infinity because that is all that there is. We got nothing because there is nothing but at least we can sing.


This is where things really go off the rails into definitely-not-mathematics-no-matter-how-you-phrase-it land. The problem is that, in the topological sense, the fact that ∞ = ∞+1 tells us something about addition- mainly that adding a small thing to a really big thing basically leaves the big thing unaffected (as opposed to saying that arctan(∞) = 90 degrees, telling us that no matter how big we make the tangent, the angle will settle towards 90 degrees). This doesn't really tell us about amounts of anything. We could more easily take set theory to deal with that, except then we get that there is a smallest set, but there is no largest set- yet still, adding one to a set might not make it bigger.

Especially with infinity, one runs into problems with finding real world consequences: in set theory, things like the axiom of infinity, which tells us that the set of natural numbers exists, are a bit hard to place in the real world. On one hand, it's kind of obvious - you can totally list the natural numbers, one at a time, and you'll never run out, but you can count up to any given natural, so it's probably okay to assume they all exist. On the other, it's hard to see what real world thing it captures - because we could never check to see that there are infinite of anything. In the topological sense, we assert that, if we wish to preserve the properties of an order, various abstract topological properties, etc., AND we wish to endow the real numbers with a greatest and least element, THEN certain things follow. This is somewhat more useful- we can talk of infinite slopes, the reciprocal of zero, and other things that might actually come up in the real world. But still, the abstraction remains and it provides insight into any real world significance it may have- but in this case, the significance of the value of f(∞) is a statement about the behavior of f, not the nature of bigness.

Further, here, you define a biggest element and a smallest element, and somehow, when it turns out that 1 is in fact that smallest natural and infinity is the biggest "number" (because you implicitly defined it as such), you weirdly declare that there is no largest and least (even though in the system you're working in, there are), then erroneously assume that since there's no biggest and smallest, nothing can be compared (just because in (0,1) we have no max or min, doesn't mean 2/3 isn't greater than 1/3). In my experience, things are bigger and hotter than others (example: the sun vs. a turtle) or faster and more abundant (i.e. mosquitoes vs. a turtle) and, at least looking locally, I can definitely orient my universe to left and right. It seems you are ignoring not only the mathematical truths you yourself assert - that a smallest and biggest thing actually exist - but also what is quite obvious in the real world. Your argument is not consistent within itself jumping from a statement to a contradiction thereof and is not consistent with observable reality. It is, in short, nonsense.

*If you wish to learn much about the foundations of math, it might come up that you need an axiom to assert the existence of a power set. When set theorists are not questioning the existence of powersets, they like to posit the existence of sets bigger than any one that may be obtained by taking power sets of the naturals repeatedly. Set theorists are weird this way, if you pretend that the field is just one guy who can't make up his mind about anything.

**We could also do with just one ∞ representing both ends of the real line. This is nice because then limit x->0 of 1/x is just infinity. This makes rational functions continuous, which is pretty sweet.

***Though actually this doesn't work. At 0*∞ there is necessarily discontinuity in multiplication, because the limit, taken in various ways, gives various answers. More accurately, we could say that f is continuous at points where it has a well-defined limit, and undefined otherwise.

Re: is mathematics a religion?

Posted: Wed Aug 06, 2014 8:43 am UTC
by 55555
Moole wrote:Further, here, you define a biggest element and a smallest element, and somehow, when it turns out that 1 is in fact that smallest natural and infinity is the biggest "number" (because you implicitly defined it as such), you weirdly declare that there is no largest and least (even though in the system you're working in, there are), then erroneously assume that since there's no biggest and smallest, nothing can be compared (just because in (0,1) we have no max or min, doesn't mean 2/3 isn't greater than 1/3). In my experience, things are bigger and hotter than others (example: the sun vs. a turtle) or faster and more abundant (i.e. mosquitoes vs. a turtle) and, at least looking locally, I can definitely orient my universe to left and right. It seems you are ignoring not only the mathematical truths you yourself assert - that a smallest and biggest thing actually exist - but also what is quite obvious in the real world. Your argument is not consistent within itself jumping from a statement to a contradiction thereof and is not consistent with observable reality. It is, in short, nonsense.


I stated the obvious fact that number 1 is smallest amount of anything. But the people to whom
I sing don't like my weird style. They refuse to accept this fact, they deny that there is such a concept, they say there is no smallest
amount, there is no smallest number they say. They say so because they are certain that there is no largest number so there can't
also be a smallest number. Quite obviously, if there is no abundance, then there is no poverty. Thus when there are no opposites,
there is nothing, not even the universe. And yes, nothing can be compared anymore.

I presented a clear statement containing these concepts, the largest and smallest numbers: Z and Y.
I asked what is their sum Z + Y equal to. Here are people with knowledge, so they say, but they did not answer my question. I even helped them by telling them that the smallest number Y=1. They did not take any notice of this. You said that:
"And why can you "tell" us that Y=1? No one has any more authority to assert things than others in math - and if calculating the sum Z+Y were possible, no hint would be necessary"
I asked that how can you calculate the sum Z + Y if you don't know what are these numbers mean. You did not want to listen what I said, you did not like my hint. You thought that I showed that I have more authority to assert things than others in math. No, that is wrong, I don't want to show that. Instead I think, I am just telling the truth, but no-one wants to listen.

If there is no smallest number, if the value of Y can be anything, then Y can also be equal to infinity. Therefore the largest amount
and the smallest amount are equal. Every thing in the universe is equal to infinity. Infinity and nothing.

I said that I drifted from forum to forum but no-one liked the weird singing style that I learned while in shower. I was told by someone that I should get voice lessons and learn how to do it right, and I took his advice at this point. I wanted to be taken seriously.

So now that learned to sing, what I sing does not seem to be consistent although I learned to sing a very good song everyone else
was singing. We are singing a song called "nothing" , it may be nonsense like you said, but you can try it at a local karaoke bar, test if the people will like your style, lyrics:"There is nothing, absolutely nothing, but it does not matter, because we hope that we will some day get a place where we can sing again, when the universe pops into existence out of the nothing,
all we got is infinity, infinitely many infinities. There is no right no wrong, no rich no poor, no slow no fast, no softness no hardness,
there is nothing but nothing, but it does not matter"

Do you think they will like the song? Would you sing it even if they did not like the song, or choose another song that they liked?
If you still think that I am singing off-key, what I can do, should I take more voice lessons?

Re: is mathematics a religion?

Posted: Wed Aug 06, 2014 10:57 am UTC
by Tirian
Lopsidation wrote:I have a friend who believes that God created mathematics. That is, if God had chosen differently, the Fundamental Theorem Of Algebra might have been false, or maybe we'd be working in a system completely different from real numbers and integers. In that way, for my friend, mathematics has a religious aspect.


I don't think that's even a particularly uncommon belief. Platonism holds that mathematical objects exist in a universe separate from our own, but that somehow we have a mystical connection to it. Therefore, you understand what I mean when I say "seven" or "circle", because we're both somehow perceiving the Seven and the Circle in that para-reality. I think it's up to you whether you believe that mathematics could have been different because of a capricious God and whether we would have found mathematics to be any less elegant if that had turned out to be the case. In any event, the conventional wisdom is that most people agree with this Platonic philosophy.

Frankly, even as a person of faith, I don't buy it. I don't believe that God gave us mathematics any more than He gave us language or art. If I can trust Wikipedia, I believe in embedded mind theories. For instance, humans created the natural numbers because in pre-history humans perceived discrete objects in the physical universe and needed a way to communicate the magnitude of collections. Addition, multiplication, and order were strategies for solving the critical real-world problems people encountered when contemplating those magnitudes. We'll never know how many times arithmetic was "invented" in the history of humanity, but it's not particularly surprising that every culture that survived came up with essentially the same answers to the same simple and straightforward questions.

Re: is mathematics a religion?

Posted: Wed Aug 06, 2014 11:38 am UTC
by gmalivuk
55555 wrote:
Moole wrote:Further, here, you define a biggest element and a smallest element, and somehow, when it turns out that 1 is in fact that smallest natural and infinity is the biggest "number" (because you implicitly defined it as such), you weirdly declare that there is no largest and least (even though in the system you're working in, there are), then erroneously assume that since there's no biggest and smallest, nothing can be compared (just because in (0,1) we have no max or min, doesn't mean 2/3 isn't greater than 1/3). In my experience, things are bigger and hotter than others (example: the sun vs. a turtle) or faster and more abundant (i.e. mosquitoes vs. a turtle) and, at least looking locally, I can definitely orient my universe to left and right. It seems you are ignoring not only the mathematical truths you yourself assert - that a smallest and biggest thing actually exist - but also what is quite obvious in the real world. Your argument is not consistent within itself jumping from a statement to a contradiction thereof and is not consistent with observable reality. It is, in short, nonsense.


I stated the obvious fact that number 1 is smallest amount of anything. But the people to whom
I sing don't like my weird style. They refuse to accept this fact, they deny that there is such a concept, they say there is no smallest
amount, there is no smallest number they say. They say so because they are certain that there is no largest number so there can't
also be a smallest number. Quite obviously, if there is no abundance, then there is no poverty. Thus when there are no opposites,
there is nothing, not even the universe. And yes, nothing can be compared anymore.

I presented a clear statement containing these concepts, the largest and smallest numbers: Z and Y.
I asked what is their sum Z + Y equal to. Here are people with knowledge, so they say, but they did not answer my question. I even helped them by telling them that the smallest number Y=1. They did not take any notice of this. You said that:
"And why can you "tell" us that Y=1? No one has any more authority to assert things than others in math - and if calculating the sum Z+Y were possible, no hint would be necessary"
I asked that how can you calculate the sum Z + Y if you don't know what are these numbers mean. You did not want to listen what I said, you did not like my hint. You thought that I showed that I have more authority to assert things than others in math. No, that is wrong, I don't want to show that. Instead I think, I am just telling the truth, but no-one wants to listen.

If there is no smallest number, if the value of Y can be anything, then Y can also be equal to infinity. Therefore the largest amount
and the smallest amount are equal. Every thing in the universe is equal to infinity. Infinity and nothing.

I said that I drifted from forum to forum but no-one liked the weird singing style that I learned while in shower. I was told by someone that I should get voice lessons and learn how to do it right, and I took his advice at this point. I wanted to be taken seriously.

So now that learned to sing, what I sing does not seem to be consistent although I learned to sing a very good song everyone else
was singing. We are singing a song called "nothing" , it may be nonsense like you said, but you can try it at a local karaoke bar, test if the people will like your style, lyrics:"There is nothing, absolutely nothing, but it does not matter, because we hope that we will some day get a place where we can sing again, when the universe pops into existence out of the nothing,
all we got is infinity, infinitely many infinities. There is no right no wrong, no rich no poor, no slow no fast, no softness no hardness,
there is nothing but nothing, but it does not matter"

Do you think they will like the song? Would you sing it even if they did not like the song, or choose another song that they liked?
If you still think that I am singing off-key, what I can do, should I take more voice lessons?

Given that you still haven't posted anything clearly defined and clearly mathematical in this thread, yes.

Re: is mathematics a religion?

Posted: Wed Aug 06, 2014 1:50 pm UTC
by schapel
55555 wrote:I stated the obvious fact that number 1 is smallest amount of anything.

Certainly the number 1 is the smallest counting number. But if I took away your last book, you would have none left, and none of something is a smaller amount than one of something. Mathematically speaking, you need to clearly define your sets before making statements about the elements they contain. When you say "number", do you mean counting numbers, natural numbers, rational numbers, real numbers, imaginary numbers, ...? And remember that numbers do not physically exist -- they are abstract, formal concepts. The number 1 is not an amount. The number 1 is a number. Do not confuse the map with the territory.
Image

Something to ponder -- if I took your book and ripped out all the pages but the last and burned them, now how many books do you have?

Re: is mathematics a religion?

Posted: Wed Aug 06, 2014 10:51 pm UTC
by kubit
schapel wrote:
55555 wrote:I stated the obvious fact that number 1 is smallest amount of anything.

Certainly the number 1 is the smallest counting number. But if I took away your last book, you would have none left, and none of something is a smaller amount than one of something. Mathematically speaking, you need to clearly define your sets before making statements about the elements they contain. When you say "number", do you mean counting numbers, natural numbers, rational numbers, real numbers, imaginary numbers, ...? And remember that numbers do not physically exist -- they are abstract, formal concepts. The number 1 is not an amount. The number 1 is a number. Do not confuse the map with the territory.
Image

Something to ponder -- if I took your book and ripped out all the pages but the last and burned them, now how many books do you have?



On top of that, if you intend to look at these things mathematically, you have to ask what one means when one says one number is less than another i.e. what kind of ordering you have. You could just as well have an ordering with nothing or 0 be the greatest number and everything else less than that or whatever.

Point here is that there is actually very little set in stone in mathematics and numbers and their orderings aren't among those things. Hence it seems bit difficult to consider mathematics as a religion when everything in it is malleable.

Re: is mathematics a religion?

Posted: Wed Aug 06, 2014 11:59 pm UTC
by PsiSquared
Forest Goose wrote:
PsiSquared wrote:
Forest Goose wrote:@55555
So, take this to heart: what you are presenting us here is, without a shred of doubt, nonsense


I won't be so quick to judge.

It is clear that 55555 is trying to pass some kind of message across. But it is also equally clear that he is utterly failing to do so. And my guess is that whatever the message is, mathematics (at least at the level 55555 understands it, given that he equates "mathematics" with ordinary numbers) is not the proper language to encode it.

Whether his point will have merit or not, once it is presented clearly - I have no idea. But let us give him the benefit of the doubt.


You do realize that, at several points, I have suggested learning more so that the idea supposed to be expressed is, indeed, being expressed. Just because someone has the intent to express something does not mean that their presentation is not nonsense. By analogy, if I knoww almost nothing about how to program, then I may intend to program a full fledged 3d open world mmorpg, but typing in random C++ terms still generates nonsense, no matter how great the idea.


True. But:

1. 55555 isn't "typing random C++ terms". A better analogy would be, trying to program a game in C++ in everyday English... without having a shred of a clue regarding what "programming" really is.

2. Humans are not computers. A C++ compiler has no choice but to regard your code as a C++ program. A human, on the other hand, can choose to decode a message in any way he wishes. And given that 55555 statements are obviously not mathematical statements, I find it counterproductive to treat them as such.

And yes, I'm fully aware of the fact that the OP himself claimed these statements to be mathematical. But he obviously doesn't know anything about mathematics, so I see no reason to take this statement as productive guidance. Obviously, he is (sloppily) using mathematical language to express non-mathematical ideas, so that is how I'm reading his posts.

Forest Goose wrote:In short, there is no "giving the benefit of the doubt" to what is written, what is written expresses nothing as is - it is not up to the audience to decode what is presented because the presenter lacked the means to do it properly - it is on the op to effectively communicate, not me to goad meaning out of them.


Of-course, you and I have no obligation what-so-ever to wreck are brains in this matter. But personally, I find statements of the kind that 55555 present here to be interesting, just because they seem "nonsense" on the face of them. I find myself wondering "what is this fellow really trying to say"?

Especially since such "weird" statements usually follow from a genuine sense of wonder about the universe. These things are what you get, when you combine natural scientific curiosity with a complete lack of scientific background. Which, I must add, I find much more compelling then all those grey "normal people" who simply carry on with their "normal lives" and don't give a hoot about the mysteries of the universe.

Re: is mathematics a religion?

Posted: Thu Aug 07, 2014 12:25 am UTC
by PsiSquared
Lopsidation wrote:I have a friend who believes that God created mathematics. That is, if God had chosen differently, the Fundamental Theorem Of Algebra might have been false, or maybe we'd be working in a system completely different from real numbers and integers. In that way, for my friend, mathematics has a religious aspect.

I'm not sure if I believe this. I can't imagine a universe where there are finitely many prime numbers. Maybe that's my fault for not being imaginative enough.


Well, any statement that starts with "if God had chosen differently..." is problematic. At least if we take, as an axiom, the traditional notion that God is omnipotent, omniscient and omnibenevolent. Since this axiom means that God is compelled - by His very nature - to always make the "right" choice, the question of "if God has chosen differently, could he..." is moot.

Re: is mathematics a religion?

Posted: Thu Aug 07, 2014 12:47 am UTC
by PsiSquared
55555 wrote:Do you think they will like the song? Would you sing it even if they did not like the song, or choose another song that they liked?
If you still think that I am singing off-key, what I can do, should I take more voice lessons?


I think, you should focus on the core message of what you're trying to say here. What are you trying to prove? What is the point?

The problem is not that you're "singing off-key". The problem is, that you're singing 3-hour serenades in a genre that your audience knows nothing about, and in a language we don't understand.

Now, the question is, what is your goal here? Is your goal to communicate your ideas effectively? Or are you simply trying to reaffirm to yourself that nobody understands you? If your goal is to communicate, than start with something short and simple. Try summarizing your main point in a single sentence. Or at least, a single paragraph.

By the way, I think that once the people here start getting the gist of what you're trying to say, it will lead to very interesting discussions (for example, set theory defines different kinds of "infinity", and the equation X+1=X doesn't hold for all of them). But first, we'll need to bridge the communication barrier. Otherwise, it will be the same old interactions you had in all those other forums, which won't do either you or us any good.

Re: is mathematics a religion?

Posted: Thu Aug 07, 2014 5:17 am UTC
by 55555
schapel wrote:Certainly the number 1 is the smallest counting number. But if I took away your last book, you would have none left, and none of something is a smaller amount than one of something.


I would say that if you have 0 books, then the amount of books you have does not exist. If you have no books, how can you say that
you have the smallest amount of books? If you have nothing, then you really have nothing, you don't even have any amount of
anything.


schapel wrote:Something to ponder -- if I took your book and ripped out all the pages but the last and burned them, now how many books do you have?


Then I would have one book with only one page.

Now ponder this, if you had an atom, lets say a gold atom, if I took your gold atom and divided it into many parts and burned all the parts but the last, now how much gold do you have?

Re: is mathematics a religion?

Posted: Thu Aug 07, 2014 5:32 am UTC
by 55555
PsiSquared wrote:I think, you should focus on the core message of what you're trying to say here. What are you trying to prove? What is the point?


I don't know why did you not get my point although I said it may times.
My point is: what is the sum Z + Y equal to?
I have explained what are Z and Y, they are the largest and smallest amounts or numbers.
Here are people with with knowledge, so they say, but they refuse to give an answer to my question.
You said that I obviously don't know anything about mathematics, meaning that obviously you know at least something
about mathematics because how otherwise you could say so. So lets hear what is your answer to my question.
I have already told that the smallest amount of anything Y=1. So now it should be an easy task for you to say
what is Z + 1 equal to ?

Re: is mathematics a religion?

Posted: Thu Aug 07, 2014 7:14 am UTC
by chridd
55555 wrote:My point is: what is the sum Z + Y equal to?
I have explained what are Z and Y, they are the largest and smallest amounts or numbers.
It depends on which number system you use:
• In the real numbers, the integers, the natural numbers, and the positive integers, there isn't a largest number at all; Z doesn't exist, Z doesn't equal anything
• In the extended real number line (which I suspect is what most non-mathematicians think of when they think of infinity; at least, it's what I thought of before learning about set theory), the largest possible number is infinity. ∞ + 1 = ∞
• In many other number systems with infinity, such as the cardinal numbers and the ordinal numbers and the surreal numbers, there are multiple infinities; in these systems, infinity is no longer the largest number, but is instead one of many infinite numbers, all of which are larger than finite numbers
• In number systems with a finite number of numbers, there could be a largest element, but what happens when you add 1 to that depends on the number system. In modular arithmetic, the largest number + 1 = 0. In saturating arithmetic, the largest number + 1 = the largest number. One could also define a system where the largest number + 1 is undefined.

Re: is mathematics a religion?

Posted: Thu Aug 07, 2014 12:18 pm UTC
by gmalivuk
55555 wrote:My point is: what is the sum Z + Y equal to?
That's not a point you're trying to make, it's a question you're trying to ask.

The problem is that it has no single answer until you define your system more carefully. At which point it can have any answer you like.

I have explained what are Z and Y, they are the largest and smallest amounts or numbers.
Here are people with with knowledge, so they say, but they refuse to give an answer to my question.
You said that I obviously don't know anything about mathematics, meaning that obviously you know at least something
about mathematics because how otherwise you could say so. So lets hear what is your answer to my question.
I have already told that the smallest amount of anything Y=1. So now it should be an easy task for you to say
what is Z + 1 equal to ?
You've decided to talk about a system whose minimum element is 1.Great. Do you not see that the minimum is 1 only because you've defined it that way?

You can similarly define Z to be literally whatever you like and have that be the maximum element of whatever set you're talking about.

Then you have to define what '+' means in this system.

Then we can tell you what Y+Z is, though of course by the time you've defined your terms, you'll have already picked what Y+Z is.

All we can say at this point, based on the things you've already defined for us, is that if it's in your set, Y+Z cannot be less than 1 (because you've defined it so that 1 is the least element of your set) and it cannot be greater than Z (because you've stated your set has one greatest element and that it is Z). It could be literally anything else in the set, including 1 and Z themselves, depending on what structure *you* decide to give it.

Re: is mathematics a religion?

Posted: Thu Aug 07, 2014 12:27 pm UTC
by gmalivuk
Also, something else to consider re. map vs. territory:

Image

Re: is mathematics a religion?

Posted: Thu Aug 07, 2014 2:58 pm UTC
by schapel
55555 wrote:
schapel wrote:Certainly the number 1 is the smallest counting number. But if I took away your last book, you would have none left, and none of something is a smaller amount than one of something.

I would say that if you have 0 books, then the amount of books you have does not exist. If you have no books, how can you say that
you have the smallest amount of books? If you have nothing, then you really have nothing, you don't even have any amount of
anything.

You can't have any fewer books than zero. You can have fewer books than one. Wasn't that my point, that one is not the smallest quantity of something you can have? You seem to be denying the concept of zero.

55555 wrote:
schapel wrote:Something to ponder -- if I took your book and ripped out all the pages but the last and burned them, now how many books do you have?

Then I would have one book with only one page.

Now ponder this, if you had an atom, lets say a gold atom, if I took your gold atom and divided it into many parts and burned all the parts but the last, now how much gold do you have?

Originally I had one atom of gold, but now I have zero atoms of gold. Once you remove protons from the nucleus, it ceases to be a gold atom. Seems simple enough to me.

The interesting thing is that modeling the number of objects as a number necessarily means that you can't represent certain events in the real world as arithmetic operations. There's no mathematical operation for fissioning a gold atom or destroying pages from a book, if your mathematical model contains only the quantity of objects you have. Additionally, mathematical operations don't necessarily have a meaning in the real world. You can take the square root of the number 2, but what is the square root of 2 apples?

Math should have one of those disclaimers that appear at the front of books or the beginning of movies: "All symbols appearing in this work are fictitious. Any resemblance to real events, past or present, is purely coincidental." Statements in mathematics are merely statements about an abstract, artificially constructed, formal system. That's the only reason we can prove anything in mathematics, because it doesn't depend on the actual, physical world in the least.

Re: is mathematics a religion?

Posted: Thu Aug 07, 2014 3:36 pm UTC
by Demki
Looking at your problem "Z is the greatest number and Y is the least, what is their sum?"
A simple solution would be to use the natural numbers with the ordering B≤A if B divides A:
1 divides all numbers so it's the least, every number divides 0 so it's the greatest, so the sum is 1.

There are people more qualified than me to help you, but I couldn't help but drop this in.

Re: is mathematics a religion?

Posted: Thu Aug 07, 2014 4:08 pm UTC
by schapel
I suppose the actual question is: "If I have a set of natural numbers from 1 to N, with the standard rules of addition over the natural numbers, what is N+1?" In this case, the operation + is not closed over the set, because adding two elements of the set gives a result that is not an element of the set.
http://en.wikipedia.org/wiki/Closure_%28mathematics%29

Re: is mathematics a religion?

Posted: Thu Aug 07, 2014 11:26 pm UTC
by PsiSquared
55555 wrote:
PsiSquared wrote:I think, you should focus on the core message of what you're trying to say here. What are you trying to prove? What is the point?


I don't know why did you not get my point although I said it may times.
My point is: what is the sum Z + Y equal to?


I'm sorry, but I still don't understand what is the actual point you're trying to make.

On the one hand, you seem to be asking a question. On the other hand, you're obviously not really "asking" anything, because you've already decided what the answer should be.


55555 wrote:I have explained what are Z and Y, they are the largest and smallest amounts or numbers.


Yes. What you didn't explain is, why? What' are you trying to prove with your line of reasoning?

Oh, and by the way, you've also never explained how come you're so sure that such Z and Y actually exist. Because in most number systems, they don't.

Here are people with with knowledge, so they say, but they refuse to give an answer to my question.


You know very well that this is untrue.

The people here have given you plenty of answers. You may not like those answers and you may diagree with them, but claiming that the people here "refuse" to answer you is simply false (not to mention rude).

You said that I obviously don't know anything about mathematics, meaning that obviously you know at least something
about mathematics because how otherwise you could say so. So lets hear what is your answer to my question. I have already told that the smallest amount of anything Y=1. So now it should be an easy task for you to say what is Z + 1 equal to ?


If it's so easy, why don''t you answer the question yourself? You obviously know what's the answer you are looking for, so why don't you just say it? Why all these games? And why, oh why, do you insist on treating the people here as if they're five-year-old morons?

Look pal, I don't care if you're the most brilliant mind to ever bless the face of earth. If you treat people with contempt, mock them, and raise false accusations against them, nobody is going to give a hoot about your ideas. So if you are really serious about effectively communicating your ideas, I strongly suggest you drop that smug attitude.

Re: is mathematics a religion?

Posted: Fri Aug 08, 2014 3:49 am UTC
by Forest Goose
@55555:

You seem more like you are presenting a koan or a riddle than anything mathematical...my recommendation is that you drop the pretense of being a singer and begin wearing a green suit with question marks (maybe you can do "+" signs):

This would work

Image.

Perhaps this (if you can work some sort of $ related gimmick into it)

Image

But, seriously, either ask a question clearly, make your point, or something - semisensical rambling interspersed with insults gets old fast; if you're going to be condescending and crankish, at least make it fun! At this point you're expected to ratchet it up a notch - talking about maximal numbers? Blagh! Start raving about the depths of infinity and how sets don't really exist because of the transcendent nature of 1 / 0. :p

Re: is mathematics a religion?

Posted: Fri Aug 08, 2014 4:58 am UTC
by 55555
PsiSquared wrote:And yes, I'm fully aware of the fact that the OP himself claimed these statements to be mathematical. But he obviously doesn't know anything about mathematics



PsiSquared wrote:
Look pal, I don't care if you're the most brilliant mind to ever bless the face of earth. If you treat people with contempt, mock them, and raise false accusations against them, nobody is going to give a hoot about your ideas. So if you are really serious about effectively communicating your ideas, I strongly suggest you drop that smug attitude.



It is you who treat people with contempt, mock them etc.
If I did not know anything about mathematics, why I should present my math ideas on a math forum?

Re: is mathematics a religion?

Posted: Fri Aug 08, 2014 5:02 am UTC
by Forest Goose
55555 wrote:If I did not know anything about mathematics, why I should present my math ideas on a math forum?


Do you know anything about mathematics? Or was the point that you don't? You do not appear to, and I don't really see the point you're trying to make with that sentence - or exactly what it means, it's not very clear - please clarify.

Re: is mathematics a religion?

Posted: Fri Aug 08, 2014 7:08 am UTC
by kubit
55555 wrote:It is you who treat people with contempt, mock them etc.
If I did not know anything about mathematics, why I should present my math ideas on a math forum?


It might be more correct to say you know too little about mathematics to be discussing the topic in this thread properly and that's what people are trying to tell you.
Either you'll have to start listening when people are telling you what mathematics is or you really have to consider stopping talking about it.

Re: is mathematics a religion?

Posted: Fri Aug 08, 2014 9:18 am UTC
by PsiSquared
55555 wrote:
PsiSquared wrote:And yes, I'm fully aware of the fact that the OP himself claimed these statements to be mathematical. But he obviously doesn't know anything about mathematics



PsiSquared wrote:
Look pal, I don't care if you're the most brilliant mind to ever bless the face of earth. If you treat people with contempt, mock them, and raise false accusations against them, nobody is going to give a hoot about your ideas. So if you are really serious about effectively communicating your ideas, I strongly suggest you drop that smug attitude.



It is you who treat people with contempt, mock them etc.


You are right regarding that one single line I wrote. And I apologize.

But that line is an exception that proves the rule. Throughout this entire discussion, I've shown genuine interest in what you are trying to say. I've asked you questions out of sincere curiosity. I've even defended you from the mockery of those few other posters who decided to treat you automatically as a crackpot, just because your language is different than the norm.

Throughout this entire discussion, most of us have shown you nothing but courtesy and respect. And what did we get in return? You treat us all as if were are five-year-old idiots. You completely ignore our answers, and then you even have the balls to claim that we "refuse to answer".

And you know what? I would have been happy to swallow all this **** from you, had you given us some serious food for thought. I'm sure you do have some very cool ideas, and it frustrates me to no end that you refuse to discuss them openly and respectfully. I mean... why start this threat at all, if you already decided from the beginning that we are all your enemies?

Re: is mathematics a religion?

Posted: Fri Aug 08, 2014 9:53 am UTC
by PsiSquared
kubit wrote:
55555 wrote:It is you who treat people with contempt, mock them etc.
If I did not know anything about mathematics, why I should present my math ideas on a math forum?


It might be more correct to say you know too little about mathematics to be discussing the topic in this thread properly and that's what people are trying to tell you.
Either you'll have to start listening when people are telling you what mathematics is or you really have to consider stopping talking about it.


The funny thing is, that 55555's philosophy seems very similar to that of Pythagoras. He rejects the notion that different axiomatic systems are possible. He believes that the only "real" mathematical entities are the natural numbers (and, perhaps, some notion of infinity, which seems to be at the crux of his whole viewpoint)

And actually, for a person with zero formal training, that's pretty good. I think we could all profit from a mutual open exchange of ideas here. I think he could profit from learning a bit about the marvels that the pros have discovered in the past 2500 years. And I thing we can profit from a fresh "naive" mind which hasn't been marred by years of formal education.

Too bad the odds of this happening, given 555555's current attitude, are close to nil.

Re: is mathematics a religion?

Posted: Fri Aug 08, 2014 11:40 am UTC
by DavCrav
PsiSquared wrote:And actually, for a person with zero formal training, that's pretty good. I think we could all profit from a mutual open exchange of ideas here. I think he could profit from learning a bit about the marvels that the pros have discovered in the past 2500 years. And I thing we can profit from a fresh "naive" mind which hasn't been marred by years of formal education.


I think you are being overly optimistic. The guy's (it's usually a guy) a crank. He could learn about real mathematics, but that's probably too hard for him, so he prefers to while away his time posting non-sensical rubbish on forums. It's true that his mind hasn't been sullied by such concepts as formal education, logic, reason or communication skills. It's not clear to me that this is a useful thing. He'll just spout pseudo-philosophical nonsense.

Re: is mathematics a religion?

Posted: Fri Aug 08, 2014 3:18 pm UTC
by schapel
Maybe this discussion is about something that confused some of my classmates in computer science: there are an infinite number of natural numbers, but all natural numbers are finite.

If you always get a natural number as a result of adding two natural numbers, then there is an endless supply of natural numbers. If I produce a natural number and claim it is the largest, you can always add 1 and prove me wrong. Therefore, there are an infinite number of natural numbers. However, each natural number can be written down in decimal form. There is no natural number that represents infinity.

If you have a set of natural numbers, it's either the case that:
1) Adding two natural numbers results in an element which is not in the set, meaning that the set is not closed with respect to addition, or
2) If the set is closed with respect to addition, there are an infinite number of natural numbers.

However, there is no natural number that represents infinity, so there is no such idea as infinity + 1 in this set with the + operator on natural numbers, because infinity is not a natural number.

I suppose the confusing concept is that the number of elements in the set of natural numbers cannot be expressed in terms of a natural number. If it were possible to do so, that number would be the largest element of the set and addition would not be closed over the natural numbers.

Re: is mathematics a religion?

Posted: Fri Aug 08, 2014 5:15 pm UTC
by Nicias
schapel wrote:Maybe this discussion is about something that confused some of my classmates in computer science: there are an infinite number of natural numbers, but all natural numbers are finite.
If you have a set of natural numbers, it's either the case that:
1) Adding two natural numbers results in an element which is not in the set, meaning that the set is not closed with respect to addition, or
2) If the set is closed with respect to addition, there are an infinite number of natural numbers.

Or the set is either empty or only contains 0.

Re: is mathematics a religion?

Posted: Fri Aug 08, 2014 5:33 pm UTC
by speising
Nicias wrote:
schapel wrote:Maybe this discussion is about something that confused some of my classmates in computer science: there are an infinite number of natural numbers, but all natural numbers are finite.
If you have a set of natural numbers, it's either the case that:
1) Adding two natural numbers results in an element which is not in the set, meaning that the set is not closed with respect to addition, or
2) If the set is closed with respect to addition, there are an infinite number of natural numbers.

Or the set is either empty or only contains 0.

but to define addition, you need at least two elements, i would think.

Re: is mathematics a religion?

Posted: Fri Aug 08, 2014 8:30 pm UTC
by gmalivuk
Addition is defined as usual, before considering the given set of numbers.

Re: is mathematics a religion?

Posted: Fri Aug 08, 2014 8:41 pm UTC
by schapel
Nicias wrote:Or the set is either empty or only contains 0.

Well, yeah, depending on whether you consider 0 to be a natural number. Wikipedia says there's no agreement on that.

But that darn empty set! I remember someone describing a student's mathematics thesis, which proved that every element of a particular set of numbers had an amazing, unbelievable property. It was an incredible result, and the proof that every element of this set did indeed have this bizarre property was ironclad. It just so happened that this set was the empty set. :o Skipping the step of proving that the set has at least one element is not wise.

Re: is mathematics a religion?

Posted: Sat Aug 09, 2014 3:57 am UTC
by Moole
speising wrote:
Nicias wrote:
schapel wrote:Maybe this discussion is about something that confused some of my classmates in computer science: there are an infinite number of natural numbers, but all natural numbers are finite.
If you have a set of natural numbers, it's either the case that:
1) Adding two natural numbers results in an element which is not in the set, meaning that the set is not closed with respect to addition, or
2) If the set is closed with respect to addition, there are an infinite number of natural numbers.

Or the set is either empty or only contains 0.

but to define addition, you need at least two elements, i would think.

Well, one's plenty. I mean the set {1} lets me add 1+1=2, which means the set's not closed - but yeah, the fact that the empty set is closed under addition is usually considered a vacuous truth - the properties is that, for every x and y in S, the sum x+y is also in S. If you can't locate any x, well, it's true no matter what you say about x. For every x in the empty set, x is a non-trivial zero of the Riemann zeta function and also a proof of the other 5 unsolved millennium problems. Technically. It's not usually terribly meaningful that it does - at least in this context (because, as you say, one couldn't really "define" addition).

But that darn empty set! I remember someone describing a student's mathematics thesis, which proved that every element of a particular set of numbers had an amazing, unbelievable property. It was an incredible result, and the proof that every element of this set did indeed have this bizarre property was ironclad. It just so happened that this set was the empty set. :o Skipping the step of proving that the set has at least one element is not wise.


I hope that student was making a math joke and not being severely disappointed after lots of work (I mean, one could never live that sort of mistake down).

Re: is mathematics a religion?

Posted: Sat Aug 09, 2014 6:10 am UTC
by Xanthir
I think it's relatively obvious what 55555 is *trying* to say - it's a variant of some basic medieval religious philosophy. Nothing is meaningful without its opposite to define it by opposition, thus for the void to exist (lack of all traits) as it demonstrably does, its opposite (the presence of all traits, or God) must also exist. Not sure what precise meaning he's trying to give to "1", but there are bunch of candidates (man, the atom, the singularity at the start of the universe). Alternately, he might just have gone with 1 as the smallest number in order to avoid the obvious solution that "Z+Y=Z, if Y=0".

It's nothing that someone who's had a freshman philosophy course hasn't been exposed to, and it's utterly uninteresting except for the mathematical crackpottery window dressing.

Re: is mathematics a religion?

Posted: Sat Aug 09, 2014 7:21 am UTC
by Forest Goose
Xanthir wrote:I think it's relatively obvious what 55555 is *trying* to say - it's a variant of some basic medieval religious philosophy.


Almost every crank I've met is either trying to use math to do philosophy or philosophy to do math, both rather poorly. I prefer the latter, wading through philosophical objections to random axioms about the reals is much much more fun - this type redefines terms a lot too, I love arguments that begin with a conceited philosophical objection to the definition of numbers and ends with the "solution" to unsolved/unsolvable problems:-)

This, here, unfortunately, is the former variety - it ends up being more a case of someone trying to use what they think is a "smart" subject to shield their cranky views from criticism (and, then, they accidentally end up believing their ridiculousness). I think the problem is that this type gets used to presenting their nonsense to the nonmathematical, who cannot debate it, which makes them feel superior - then that feeling, in turn, brings them to try the same gimmick with people who study math...that does not go so well. The sad part is, though, that you can't turn this type of person around; their original philosophical junk is to obscured to debunk and the math doesn't mean anything to them, so the only thing you can show is outright goofy is something they don't see as central to their point - hence, it's futile and , as such, more tedious than enjoyable (I like talking to the cranky - I've been borderline cranky before - it's good fun).

Anyways, sorry to go off on a rant.

Re: is mathematics a religion?

Posted: Sat Aug 09, 2014 12:10 pm UTC
by speising
Xanthir wrote:I think it's relatively obvious what 55555 is *trying* to say - it's a variant of some basic medieval religious philosophy. Nothing is meaningful without its opposite to define it by opposition, thus for the void to exist (lack of all traits) as it demonstrably does, its opposite (the presence of all traits, or God) must also exist. Not sure what precise meaning he's trying to give to "1", but there are bunch of candidates (man, the atom, the singularity at the start of the universe). Alternately, he might just have gone with 1 as the smallest number in order to avoid the obvious solution that "Z+Y=Z, if Y=0".

It's nothing that someone who's had a freshman philosophy course hasn't been exposed to, and it's utterly uninteresting except for the mathematical crackpottery window dressing.


so, if everything must have its opposite, what is the opposite of 5? we could define it as 1/x, but then the opposite of 1 would be 1. (and 1/0 is of course not infinity)

Re: is mathematics a religion?

Posted: Sat Aug 09, 2014 1:24 pm UTC
by brenok
speising wrote:
Xanthir wrote:I think it's relatively obvious what 55555 is *trying* to say - it's a variant of some basic medieval religious philosophy. Nothing is meaningful without its opposite to define it by opposition, thus for the void to exist (lack of all traits) as it demonstrably does, its opposite (the presence of all traits, or God) must also exist. Not sure what precise meaning he's trying to give to "1", but there are bunch of candidates (man, the atom, the singularity at the start of the universe). Alternately, he might just have gone with 1 as the smallest number in order to avoid the obvious solution that "Z+Y=Z, if Y=0".

It's nothing that someone who's had a freshman philosophy course hasn't been exposed to, and it's utterly uninteresting except for the mathematical crackpottery window dressing.


so, if everything must have its opposite, what is the opposite of 5? we could define it as 1/x, but then the opposite of 1 would be 1. (and 1/0 is of course not infinity)

I know it has nothing to do with any pseudophilosophical interpretation, but the opposite of 5 is -5. 1/5 would be its inverse.

Re: is mathematics a religion?

Posted: Sat Aug 09, 2014 2:11 pm UTC
by speising
but the the opposite of 0 is just 0...

Re: is mathematics a religion?

Posted: Sat Aug 09, 2014 3:53 pm UTC
by gmalivuk
brenok wrote:I know it has nothing to do with any pseudophilosophical interpretation, but the opposite of 5 is -5. 1/5 would be its inverse.
Mathematically, -5 is its additive inverse and 1/5 is its multiplicative inverse. I'm not sure "opposite" has any technical definition to begin with.

Re: is mathematics a religion?

Posted: Sat Aug 09, 2014 4:09 pm UTC
by schapel
Moole wrote:I hope that student was making a math joke and not being severely disappointed after lots of work (I mean, one could never live that sort of mistake down).

The way I heard the story, it was something the student spent many months on and gave a presentation on. But I heard the story second hand, so it could be an urban legend.

speising wrote:but the the opposite of 0 is just 0...

Whoa, you just blew my mind, man!