## Search found 180 matches

- Thu Feb 09, 2017 1:54 pm UTC
- Forum: Mathematics
- Topic: "There is an Exception to every rule"
- Replies:
**32** - Views:
**8750**

### Re: "There is an Exception to every rule"

That's not a rule, that's a tautology. Fine, for every prime p, and every integer a prime to p, a raised to power p minus a is divisible by p. Not a tautology, definitely no exceptions. Happy now? If you mean "For every prime p and integer a coprime to p , ( a p - a ) | p ," then that is ...

- Tue Oct 04, 2016 10:07 pm UTC
- Forum: Mathematics
- Topic: Factorization using modular arithmetic
- Replies:
**41** - Views:
**11389**

### Re: Factorization using modular arithmetic

Here is a way to solve quadratic congruence using very very elementary tools (no Euclidean algorithm, no Euler theorem, no inverse computing etc...). This method could be coded and improved. Quadratic congruence General form : a*x^2= b mod c (c odd prime) gcd(a,c)=1 Example : Solve : 37*x^2=13 mod ...

- Fri Jun 03, 2016 5:02 am UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**75922**

### Re: Misunderstanding basic math concepts, help please?

I won't argue with #1 because that's an argument which has very little to do with mathematics (and this will likely to get our moderators angry again). But I will strongly argue against your second point. The questions that Treatid asked can be answered adequetly (and more-or-less rigorously) in si...

- Sun May 29, 2016 6:32 am UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**75922**

### Re: Misunderstanding basic math concepts, help please?

Just so that we know what we are talking about, could Treatid please ⋅ Describe formally some particular axiomatic system (eg. Peano Arithmetic, including the background logic system, say, first order logic of some sort) ⋅ State precisely the law of excluded middle in that axio...

- Wed May 25, 2016 8:59 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**75922**

### Re: Misunderstanding basic math concepts, help please?

In axiomatic mathematics 'provable' and 'true' are the same thing. If it can be proven (with respect to the axioms) then it is true (with respect to the axioms). No. ETA: provability is a well-defined concept, namely that there is a proof. There are many ways we can define truth. If we define "...

- Sun May 22, 2016 2:43 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**75922**

### Re: Misunderstanding basic math concepts, help please?

A proposition could have: 1. Just two possible states: True or not-true. 2. Many possible states: True, not-true and things that are either 'neither true or not-true' or 'both true and not-true'. 3. Many possible states: things that are neither true or not-true (true and false not being valid state...

- Wed May 11, 2016 8:55 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**75922**

### Re: Misunderstanding basic math concepts, help please?

In logic, the law of excluded middle (or the principle of excluded middle) is the third of the three classic laws of thought. It states that for any proposition, either that proposition is true, or its negation is true.- Before we get on to more complicated logic... it appears I can't read this sim...

- Mon May 09, 2016 5:50 am UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**75922**

### Re: Misunderstanding basic math concepts, help please?

Sorry to load it on but I'm not going to respond unless you correctly answer 2 of the problems on this logic worksheet. http://cw.routledge.com/textbooks/9780415997454/printable-exercise-worksheets/chapter4/web-ch4-4-exer-D.pdf edit: Actually don't do that worksheet unless you want to. We don't nee...

- Tue May 03, 2016 5:58 am UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**75922**

### Re: Misunderstanding basic math concepts, help please?

I think you should get a book and actually learn how things are actually done, instead of just speculating without actually knowing the subject you are talking about. Once you have actually learnt how logic is done in modern days, we can discuss about the technical aspects of it.

- Sat Apr 30, 2016 7:45 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**75922**

### Re: Misunderstanding basic math concepts, help please?

I think I agree, but on this point we need to be very careful. The word "Axiom" is getting thrown around a bit loosely here. I think we should reserve the word "axiom" to mean the following: Assume we have a formal langauge with symbols and syntax. Construct a number of well for...

- Sat Apr 30, 2016 6:20 am UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**75922**

### Re: Misunderstanding basic math concepts, help please?

One of the goals (sort of) of mathematical rigor is to minimize the amount that we take for granted by using only some of the most ingrained intuitions in the way the human mind works. Things like basic logical inference (If I know 'A' is true and I also know "if A then B", then I can con...

- Fri Feb 05, 2016 1:20 pm UTC
- Forum: Religious Wars
- Topic: 1/xy
- Replies:
**12** - Views:
**10513**

### Re: 1/xy

Flumble wrote:Infix notation is stupid to begin with –it only really works for commutative associative operators. Polish or graph notation FTW!

Subtraction?

- Fri Feb 05, 2016 8:05 am UTC
- Forum: Mathematics
- Topic: Well-ordered Subset of Reals
- Replies:
**8** - Views:
**3041**

### Re: Well-ordered Subset of Reals

So the question is: Does every countable ordinal have a fundamental sequence? (I tried to look up the answer in google and Wikipedia, and found nothing) Yes. Proof is left as an exercise for the reader (hint: list out everything smaller than your ordinal, and then try to create an increasing sequen...

- Sat Jan 23, 2016 2:10 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1633: "Possible Undiscovered Planets"
- Replies:
**104** - Views:
**17257**

### Re: 1633: "Possible undiscovered planets"

xkcd wrote:Planets ruled out because~~we would see them during the day~~it would be day when we see them.

- Fri Dec 25, 2015 7:57 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1621: "Fixion"
- Replies:
**19** - Views:
**6731**

### 1621: "Fixion"

Title text: "My theory predicts that, at high enough energies, FRBs and perytons become indistinguishable because the detector burns out."

So this is what they found at CERN.

- Mon Oct 05, 2015 12:47 pm UTC
- Forum: Mathematics
- Topic: Axioms and multiplication?
- Replies:
**18** - Views:
**3565**

### Re: Axioms and multiplication?

To answer you first question, anything that is a complete ordered Archimedean field is isomorphic to the real numbers. Fixed that for you. Pretty sure you get Archimedean from complete, as it says here https://en.wikipedia.org/wiki/Construction_of_the_real_numbers#Synthetic_approach Usually "c...

- Wed Aug 05, 2015 1:48 pm UTC
- Forum: Computer Science
- Topic: the halting problem
- Replies:
**16** - Views:
**7593**

### Re: the halting problem

Well, from various places, including the wikipedia article. Can you tell me how it is different from mine ? Wikipedia's h is the same as my h, my x(i,i) would be wikipedia's g(i), with only inverting the output value, but it does not seem relevant as the point is just to see wether it halts or not....

- Wed Aug 05, 2015 1:33 pm UTC
- Forum: Computer Science
- Topic: the halting problem
- Replies:
**16** - Views:
**7593**

### Re: the halting problem

For example, you could be passing x as a string (the source code), and x-as-a-program runs some checks on the string to decide whether it halts or not. Ok, but with what inputs? By definition, x halts or not depending on its input. Here, x is supposed to decide wether x halts or not. But with which...

- Wed Aug 05, 2015 1:11 pm UTC
- Forum: Computer Science
- Topic: the halting problem
- Replies:
**16** - Views:
**7593**

### Re: the halting problem

That is a function that does not use its input. What does it have to do with my question? It doesn't matter. Your function x does not have to evaluate itself with itself as an input. It merely receives the program and input, and checks whether it halts. For example, you could be passing x as a stri...

- Wed Aug 05, 2015 12:25 pm UTC
- Forum: Computer Science
- Topic: the halting problem
- Replies:
**16** - Views:
**7593**

### Re: the halting problem

Yat wrote: OK, but x has inputs, so how exactly are we supposed to feed x to itself?

Why not? Real world example that does not explode:

Code: Select all

`def func (input):`

print("Hello World!")

return

func(func) # Prints Hello World!

- Sat Jun 20, 2015 12:15 pm UTC
- Forum: Mathematics
- Topic: Leading numbers
- Replies:
**8** - Views:
**2479**

### Re: Leading numbers

Chinese Remainder Theorem?

- Sat Jun 06, 2015 9:06 pm UTC
- Forum: Serious Business
- Topic: Should religion be illegal for children?
- Replies:
**289** - Views:
**67288**

### Re: Should religion be illegal for children?

[Religion] is also capable of having consequences that are just as serious. Please explain. Also, I believe "watching porn" is a better analogy than "having sex/aquiring debt etc", since we are talking about blocking children from some sort of information that we think they shou...

- Mon Jun 01, 2015 12:37 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1532: "New Horizons"
- Replies:
**23** - Views:
**6427**

### Re: 1532: "New Horizons"

Steve: "But it works in Kerbal Space Program!"

- Sat May 30, 2015 7:04 am UTC
- Forum: Coding
- Topic: Useful applications of recursion?
- Replies:
**19** - Views:
**5268**

### Re: Useful applications of recursion?

Recursion is useful when you want to recurse into tree-like structure, eg. if you want to check if there is an element of the tree named "foo", you might have def check(node): if node.name == "foo": return True for child in node: if check(child): return True return False Alternat...

- Mon Apr 20, 2015 11:34 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1513: "Code Quality"
- Replies:
**81** - Views:
**19575**

### Re: 1513: "Code Quality"

orthogon wrote:just like a word processor/IDE is probably better for large documents/software projects.

I'm yet to see a word processor that handles large documents.

- Mon Mar 30, 2015 4:14 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1505: "Ontological Argument"
- Replies:
**278** - Views:
**41917**

### 1505: "Ontological Argument"

http://imgs.xkcd.com/comics/ontological_argument.png Title text: "A God who holds the world record for eating the most skateboards is greater than a God who does not hold that record." Yeah but Zorn's lemma entails that we can find a being of maximal greatness, which would be god.

- Wed Feb 11, 2015 1:23 pm UTC
- Forum: Mathematics
- Topic: How do axioms specify a new system vs continuing an old one?
- Replies:
**81** - Views:
**10443**

### Re: How do axioms specify a new system vs continuing an old

The difference between quantifying over predicates and using axiom schemas is that if you use axiom schemas in a proof, you use them one by one. If you quantify over predicates, you use all instances of the axioms schemas all at once. This makes a difference when your proofs have to be finite.

- Fri Jan 02, 2015 10:30 am UTC
- Forum: What If?
- Topic: What-If 0123: "Fairy Demographics"
- Replies:
**25** - Views:
**11367**

### Re: What-If 0123: "Fairy Demographics"

Footnote [6] ignores the possibility of fairy truthers. Clearly all this "well-documented" evidence about fairies is just a false flag operation. Truthers? I thought fairy truthers believe in the existence of fairies? Anyway, in that case they would be repeating that deadly phrase much mo...

- Mon Dec 29, 2014 7:01 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1466: "Phone Checking"
- Replies:
**23** - Views:
**7044**

### Re: 1466: "Phone Checking"

Is Randall secretly conducting this competition for the What-If site?

- Wed Dec 24, 2014 6:57 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1464: "Santa"
- Replies:
**62** - Views:
**12639**

- Tue Nov 18, 2014 8:40 pm UTC
- Forum: What If?
- Topic: What-If 0119: "Laser Umbrella"
- Replies:
**46** - Views:
**21903**

### Re: What-If 0119: "Laser Umbrella"

Apparently 3 people made entries for "autoclave you can live in" after the what-if came out. The list was initially empty.

- Fri Nov 14, 2014 10:04 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1447: " Meta-Analysis"
- Replies:
**42** - Views:
**12739**

### Re: 1447: " Meta-Analysis"

meta^{\omega_0}-analysis

- Sat Oct 04, 2014 4:43 am UTC
- Forum: News & Articles
- Topic: Hong Kong: Streets blocked as pro-democracy protests spread
- Replies:
**46** - Views:
**11117**

### Re: Hong Kong: Streets blocked as pro-democracy protests spr

Some of the anti-occupy mob are probably hired from mainland, but many are actually from HK. The triads have interests in many shops in Mong Kok area and the protests affect their income. The clashes were pretty much inevitable. You can't ignore the possibility that someone hired the triads. Should...

- Wed Oct 01, 2014 6:02 am UTC
- Forum: News & Articles
- Topic: Hong Kong: Streets blocked as pro-democracy protests spread
- Replies:
**46** - Views:
**11117**

### Re: Hong Kong: Streets blocked as pro-democracy protests spr

I hope Hong kong protest succeeds in its mission , but i doubt they will last long in front of Chinese bullies . :( From what I've seen, I'd say it's the other way round. The reason why there are so many people on the streets is the police treated the initial protesters too harshly and caused outra...

- Tue Sep 30, 2014 10:10 pm UTC
- Forum: News & Articles
- Topic: Hong Kong: Streets blocked as pro-democracy protests spread
- Replies:
**46** - Views:
**11117**

### Re: Hong Kong: Streets blocked as pro-democracy protests spr

I know the agreement was they'd be largely autonomous for sometime (up to 2047?). I've heard that this 50-year thing (Hong Kong will remain autonomous 1 for 50 years till 2047) is a metaphorical answer meaning "a long time" when Deng Xiaoping was asked about the question. It ended up writ...

- Tue Sep 30, 2014 4:51 am UTC
- Forum: News & Articles
- Topic: Hong Kong: Streets blocked as pro-democracy protests spread
- Replies:
**46** - Views:
**11117**

### Re: Hong Kong: Streets blocked as pro-democracy protests spr

However, thousands of bodies in Hong Kong will considerably hurt the money train. Right now countries are staying out of it, but if it escalates to that point, the international community is going to explode in anger. And, I assume, it's probably going to be worse than the Tiananmen reaction, for s...

- Tue Sep 30, 2014 12:00 am UTC
- Forum: News & Articles
- Topic: Hong Kong: Streets blocked as pro-democracy protests spread
- Replies:
**46** - Views:
**11117**

### Re: Hong Kong: Streets blocked as pro-democracy protests spr

Mutex wrote:I thought what they wanted was for Beijing not to have the power to veto each candidate to stand for power in HK.

The third requirement I listed above? The NPC's decision was that Beijing has (in effect) the power to veto each candidate. And the protesters wanted Beijing to take back that decision.

- Mon Sep 29, 2014 10:33 pm UTC
- Forum: News & Articles
- Topic: Hong Kong: Streets blocked as pro-democracy protests spread
- Replies:
**46** - Views:
**11117**

### Re: Hong Kong: Streets blocked as pro-democracy protests spr

I wonder how long the protests will last before the authorities decide to crack down again. I'm not sure if the authorities can do anything to them unless they actually shoot. When the police used the tear gas, the people did indeed disperse. Yet after the gas dissapated, they returned to their ori...

- Mon Sep 29, 2014 5:58 am UTC
- Forum: News & Articles
- Topic: Hong Kong: Streets blocked as pro-democracy protests spread
- Replies:
**46** - Views:
**11117**

### Hong Kong: Streets blocked as pro-democracy protests spread

http://www.bbc.com/news/world-asia-china-29405195 What the protesters did: stand there, hands up (http://youtu.be/aFaXy3xbrkQ?t=2m6s) What the police did: tear gas, pepper sprays (also: stealing the umbrellas protesters used for blocking the pepper spray http://youtu.be/h64lJB_5qjc?t=1m9s), draggin...

- Fri Sep 26, 2014 5:10 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1426: "Reduce your payment"
- Replies:
**35** - Views:
**13306**

### Re: 1426: "Reduce your payment"

chenille wrote:I've also heard there is a weird trick to kill belly fat, and now I'm certain I don't want to know any more about it.

Handgun?