## Search found 23 matches

Wed Jul 08, 2015 4:06 pm UTC
Forum: Mathematics
Topic: Wanted: Elegant proof of sin(x)/x limit
Replies: 49
Views: 8952

### Re: Wanted: Elegant proof of sin(x)/x limit

Nicias wrote:
kubit wrote:Is the some reason we don't want to apply L'Hospital's rule?

L'Hospital's rule requires the derivative of sin(x), which requires knowledge of this limit.

Using L'H in this case is begging the question.

Doh.. such a brain fart from me. How about using sin(x) series expansion?
Wed Jul 08, 2015 12:37 pm UTC
Forum: Mathematics
Topic: Wanted: Elegant proof of sin(x)/x limit
Replies: 49
Views: 8952

### Re: Wanted: Elegant proof of sin(x)/x limit

Is the some reason we don't want to apply L'Hospital's rule?
Fri Jun 05, 2015 2:44 pm UTC
Topic: 1534: "Beer"
Replies: 249
Views: 62575

### Re: 1534: "Beer"

Wow, those guys are seriously drinking the wrong kind of beer. The kind with hops in it? Because that's what makes beer taste so bad, and it's pretty much required by most definitions of "beer". Hops are terrible. A bit of it can add to a beer but many beers have far to much hops. Especia...
Thu May 21, 2015 11:17 pm UTC
Forum: Mathematics
Topic: Statistics. Conditional probability and percentage.
Replies: 4
Views: 2017

### Re: Statistics. Conditional probability and percentage.

Hi, I have the following exercise on conditional probability: Suppose 60% of the freshmen class of a college are women. Furthermore, suppose 25% of the men and 10% of the women in the class are studying mathematics. A freshman student is chosen at random. Find the probability that: The student is s...
Sat Aug 09, 2014 4:55 pm UTC
Forum: Mathematics
Topic: questions from algebra (inverse functions)
Replies: 25
Views: 4841

### Re: questions from algebra (inverse functions)

mike-l wrote:Yes, but now you are indeed using precisely what I said in the first place, equivalence classes of set isomorphisms.

Technically yea, that's one way to put it. I was bit tired when I wrote my earlier responses.. sorry about that. Hopefully we are in the clear now
Sat Aug 09, 2014 10:45 am UTC
Forum: Mathematics
Topic: questions from algebra (inverse functions)
Replies: 25
Views: 4841

### Re: questions from algebra (inverse functions)

I understand what limit ordinals are. But most limit ordinals are not of different cardinalities. Eg omega is the first countably infinite ordinal, but omega*n is also a limit ordinal of the same cardinality. In fact there are infinitely many limit ordinals that are still countable. In fact there a...
Fri Aug 08, 2014 9:28 pm UTC
Forum: Mathematics
Topic: questions from algebra (inverse functions)
Replies: 25
Views: 4841

### Re: questions from algebra (inverse functions)

I'm a little confused by this, as there are many limit ordinals of the same cardinality. Maybe you meant initial ordinal, but I'm not aware of a definition of these that doesn't refer to cardinality. Also there are many bijections that respect the structure of the source space but aren't isomorphis...
Fri Aug 08, 2014 7:08 am UTC
Forum: Mathematics
Topic: is mathematics a religion?
Replies: 82
Views: 16739

### Re: is mathematics a religion?

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 ...
Fri Aug 08, 2014 6:55 am UTC
Forum: Mathematics
Topic: questions from algebra (inverse functions)
Replies: 25
Views: 4841

### Re: questions from algebra (inverse functions)

Huh. Maybe it's the fact that I think mostly in terms of category theory, but I find that usage both natural and common. What do you think of cardinalities as being? I think of them as isomorphism classes of sets. The rest of the post is beyond the scope of the original question, and can safely be ...
Thu Aug 07, 2014 9:28 pm UTC
Forum: Mathematics
Topic: questions from algebra (inverse functions)
Replies: 25
Views: 4841

### Re: questions from algebra (inverse functions)

Oh woah.. I have never seen isomorphism defined that way. Sure you can do that, but usually isomorphism is defined in relation to some kind of structure or feature of the set rather than just in relation to the size of the set. I mean that kind of definition seems to me as it just labels isomorphism...
Thu Aug 07, 2014 4:24 pm UTC
Forum: Mathematics
Topic: questions from algebra (inverse functions)
Replies: 25
Views: 4841

### Re: questions from algebra (inverse functions)

by the way, if f bijects A, B means A and B are isomorphic, doesn't |A| = |B| imply A and B are isomorphic and vice versa? since for all bijections, the size of both sets must be equal. in addition, any two equally sized sets can be bijected by randomly pulling singletons from them If two sets have...
Wed Aug 06, 2014 10:51 pm UTC
Forum: Mathematics
Topic: is mathematics a religion?
Replies: 82
Views: 16739

### Re: is mathematics a religion?

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 ...
Sun Aug 03, 2014 9:17 pm UTC
Forum: Mathematics
Topic: questions from algebra (inverse functions)
Replies: 25
Views: 4841

### Re: questions from algebra (inverse functions)

g needs to map B to A. so sqrt(x) would be a right inverse of x^2. i think. and to prove g exists: the graph of f is a collection of ordered pairs where the set of the second element in each of the pairs is B, and the set of the first element in each of the pairs is A. we know this is true because ...
Fri May 16, 2014 9:14 pm UTC
Forum: Mathematics
Topic: Need second opinion. I think I disproved God.
Replies: 72
Views: 12949

### Re: Need second opinion. I think I disproved God.

My argument wasn't about a particular god or a particular religion. And if religious people are allowed to keep coming up with new religions and new defintions of God, day by day, year by year, then I am allowed to use a generic god as an example. Doesn't it seem bit silly that you'd define your ow...
Fri May 16, 2014 11:25 am UTC
Forum: Mathematics
Topic: Need second opinion. I think I disproved God.
Replies: 72
Views: 12949

### Re: Need second opinion. I think I disproved God.

My argument wasn't about a particular god or a particular religion. And if religious people are allowed to keep coming up with new religions and new defintions of God, day by day, year by year, then I am allowed to use a generic god as an example. Doesn't it seem bit silly that you'd define your ow...
Sun Nov 10, 2013 12:59 am UTC
Forum: Mathematics
Topic: Dogma in Math
Replies: 98
Views: 14671

### Re: Dogma in Math

I'm using parentheses around nothing to represent an empty set, which I believe (and could be mistaken) is unique from the "number" zero. Actually, in the set theoretic construction of the natural numbers, the empty set is usually considered to be the number zero and the first ordinal num...
Sat Sep 21, 2013 11:17 am UTC
Topic: On the limits of language and definability
Replies: 28
Views: 8122

### Re: On the limits of language and definability

Putting the subset of the question of language to one side, the answer to the question "is it possible that there are aspects to the universe that follow no logical structure?" then the answer has to be yes the thing that people largely gloss over is that rather than being a deep question...
Fri Sep 20, 2013 1:52 pm UTC
Topic: On the limits of language and definability
Replies: 28
Views: 8122

### Re: On the limits of language and definability

Problem with this is that all our perception of the world is 'subjective' in the end. Any knowledge we have is subjective because it has to be processed first in our minds. We don't have anything that is directly attached to reality. Only images constructed by our brain. We don't really have a bett...
Fri Sep 20, 2013 1:37 pm UTC
Topic: On the limits of language and definability
Replies: 28
Views: 8122

### Re: On the limits of language and definability

To me it seems plausible that there might be things that are real that are simply beyond the extent of 'human' logic. And if they are beyond human logic they are beyond any logical language that could be understood by humans as well. Therefore one wouldn't be able to speak about them by definition....
Fri Sep 20, 2013 1:10 pm UTC
Topic: On the limits of language and definability
Replies: 28
Views: 8122

### Re: On the limits of language and definability

Humans can very definitely have experiences that are difficult/impossible to put into words - mind-altering drugs and deep spiritual experiences are obvious examples. But by their very nature they're purely subjective experiences and don't represent any kind of 'physical reality'. Problem with this...
Fri Sep 20, 2013 12:28 pm UTC
Topic: On the limits of language and definability
Replies: 28
Views: 8122

### On the limits of language and definability

Heya, did a search on this and couldn't find anything similar. If it's just my failure please give me boot to the head. I'm a new one here! I was reading Wittgenstein a while back(just for fun, not studying philosophy or anything) and was inspired to some extent regarding what language can or cannot...
Wed Sep 18, 2013 3:20 pm UTC
Forum: Religious Wars
Topic: Math or Science
Replies: 65
Views: 54337

### Re: Math or Science

Math takes the cake here as far as I am concerned. Science, especially physics, is merely a mathematical way to predict things. It doesn't give us any real 'knowledge' of reality. It only gives us ways to predict what might be happening next. :P The only conclusion you can draw from scientific testi...
Fri Sep 06, 2013 6:24 pm UTC
Forum: Mathematics
Topic: The Tau Manifesto
Replies: 165
Views: 44041

### Re: The Tau Manifesto

Just to put my two cents worth in... I'm fairly sure mathematics education has far more important problems these days than whether 2pi has its own symbol! Really, even though I agree that there is a point with tau being more intuitive in geometry it seems like major waste of time to argue over it...