The Maths Topic

I don’t understand your post. Maybe my english is bad so i’ll rephrase it:

Theorem: 1 is the largest natural number.

Proof:
Suppose the largest natural number is N. Then if N > 1 we have N^2 > N contradicting the definition (of N). Hence N = 1.

qed

Do you agree with this proof?

Well, at first Im not good at math.

As second, i never heard about greates number. There is infinity of natural numbers, so N just does not exist. Am i right ?

Yes that’s the problem. The proof is correct but you can prove anything about something that does not exist.

You cannot say “I have a natural number. I make it bigger. But I assumed the natural number was the biggest one! Therefore 1 is the biggest!” it’s an mathematically illegal statement. It more says “This proof says there is always a natural number higher than N.”

l…e…t…t…e…r…s…
/me faints*

Arrgh! I feel like such a dumb-ass with all you guys saying all this stuff, like it’s common sense :cry:

no one seems to have answered what i posted (page 2) >.>

I have been wodering
People do this x^2 to show two times x.
The way I learned it was 2x.
Why?

x^2 is not 2x. It’s x to the power 2, which is x times x.

Theorem: All natural numbers are extremely interesting

Proof: By contradiction, let’s assume that N is the first really boring natural number.
But it is the smallest boring natural number. Being the smallest boring natural number is an interesting property of N. So N is actually an interesting natural number!

:wink:

i love math :smile:

Grr, I still don’t get it. As long as you perform the square root on both sides it has to be valid right?

Mathematical proof that all girls are evil:

First, let’s state that the number of girls you get is proportional to the time and money you invest. Therefore:

(Girls) = (Time) x (Money)

Time is money: (Time) = (Money), so:

(Girls) = (Money) x (Money), or:
(Girls) = (Money)²

[i]Money is the root of all evil: /i = sqrt(Evil), so:

(Girls) = (sqrt(Evil))², therefore:
(Girls) = (Evil)
qed

@up
Einstiein bows before you in his grave

Has anyone heard of the Trinegulance Theory? It deals with immense probabilities and sub-ords in a rigorous fashion.

A sample of the theory would state if L^10(M)-10(^N) then LMN(N-M^10[L]) will remain true to its negative (reversed) answer… oh the beauty of mathematics!

I have pi memorised to 362 places. :smile: Pi is infinite (I’ve read books on it!), it can’t end. You can’t say ‘x’ = pi, because we don’t know what pi fully is. Sure, you can say x = 3.14, but that’s nothing spectacular - it proves nothing. You can’t say that x = pi, because pi never ends. Ever.

Anyone know of the Riemann hypothesis? Prime numbers are more intricate than you may think!

I’ve studied the Riemann hypothesis and the theory of the Riemann zeta function extensively for the last six years (since i was 16!)
I can’t say i have any idea about how to prove it :tongue:
but i find it fascinating!
i’m pretty sure the proof will be based on totally new maths, just like the proof the Fermat’s Last Theorem.

Okay. Now that I know calculus:

The assumption here is that the derivative 1 + 1 + . . . + 1 (x 1’s) is in fact 0 + 0 + . . . + 0 (x 0’s), but it isn’t–use the product rule or something, if you want. The fact that there’s an “x” in there means you can’t just differentiate the zeros.

Now, don’t say “well, for some constant c, c = x, so it’s 1 + 1 + . . . + 1 (c 1’s) = x, which you can differentiate to 0 + 0 + . . . + 0 (c 0’s) = 1”. In calculus, you’re just not allowed to set something to a constant and then differentiate over it.

Edit: oh, and:

Yes, you can say x = pi: pi is a real number, just like 3.14. Sure, pi’s decimal expansion never ends, but pi does have definitions which do end. An example: pi is the sum as n goes from 0 to infinity of (4/(1+4n) - 4/(3+4n)).

Oh, given that a day has passed, I think making a new post for this is best.

The theory goes that if something involves accomplishment, you can enjoy it. (Actually, that’s just my own theory, but it seems to work fine.) I’m guessing by your belief that you can make 100 cents equal 1 cent that you believe it’s possible to do anything at all within math, correct?

Things such as the 1 cent = 100 cents thing are essentially mathematical jokes or puzzles: the point of those is to figure out what’s wrong with them. Mathematics at its core essentially consists of “if this is true, then this is true”, so it’s all about questions such as “is this true?”, “when is this true?”, and “what’s wrong with this?”.

Now, there’s more to math than just numbers–in fact, the things dealt with in math are best described as being just “things”. If you want to define, say, a real number, first you come up with some basic things you can do with real numbers: you can add them, you can multiply them, and you can compare them to see which is bigger (or if they’re equal). Then you decide on a list of properties you want the real numbers to have. Given enough rules about how +, * and > work, you end up with a definition of a real number, and from then you can define anything about them. Here’s a definition of a whole number (as distinguished from an integer):

  • There is a whole number that is not the successor of any whole number–call it zero.
  • For every whole number, there is a whole number that is the successor of that whole number.
  • If something is true for zero, and for every whole number it’s true for, it’s also true for that whole number’s successor, then it’s true for all whole numbers.

This uses the successor function as the only “primitive”, and defines other things, such as zero, based on this primitive. We can then define anything we want that can be done with whole numbers: addition, multiplication, factorials… we can define subtraction, though sometimes subtraction doesn’t work: -2 is not a whole number.

My point, I guess, is that math is all about rules and proving that they imply things–proving something or otherwise finding something out sounds like an accomplishment to me, especially if you can use it. Occasionally I go to Wikipedia and look for interesting things, often mathematical things. There’s set theory, category theory, real analysis, computer science, topology, cryptology… there are probably whole big fields of mathematics I haven’t even heard of. Lots of stuff to it, and it’s certainly more fun if you understand it.

Square roots as in turning x^2 into x aren’t a function, so you can’t do that to both sides. Consider this false proof, which isolates the problem:

4 = 4
2^2 = (-2)^2
2 = -2

It’s true you know :content: