Math problem

Originally posted by mtthw
Probably 🙂

I suspect proofs using the set theory definitions of cardinal numbers might be more interesting, but I don't remember much set theory!

Using the Axioms of Zermelo and Fraenkel;

Using S(A) to denote the sucessor of A and BU to denote the Big Union
For all ordinals A and B and all limit-ordinals L addition is defined with the following;

A + 0 = A
A + S(B) = S(A+B)
A + L = BU{ A+B | B in L}

Using that on 1 + 2;

1 + 2 = 1 + S(1) = S( 1 + 1 ) = S( 1 + S(0) ) = S( S( 1 + 0 ) ) = S( S( 1 ) ) = S( 2 ) = 3

Originally posted by joe shmo
Is that the problem Which leads to 1 when performing the operations, If it is, then I ve read that they are offering a reward for it proof!

i was under the impression that there was a reward for it since a while back

Originally posted by banx99
i was under the impression that there was a reward for it since a while back

Yes, I guess since 1937 here's a link for more info

http://mathworld.wolfram.com/CollatzProblem.html

Originally posted by Jirakon
What about the points that define a circle with a radius of infinity?

That's the first thing that came to mind. It would have to be infinite, since if it were a finite number of points, one could easily draw a horizontal line far above the last point. I'm pretty sure that's the solution.

Infinities don't exist 🙁

Originally posted by wolfgang59
Just because all points have finite coordinates does not mean there is a 'y-max'

Otherwise your "proof" could be used to prove that the set of points on x=0 is finite.

I disagree. His proof only proves that the line x=1 does not intersect two of the points in that set.

Originally posted by Palynka
I don't see why what I said implies the set must be bounded. Take the Euclidean axis. No line that you can draw or represent as a function intersects a point of those axes only at infinity.

But there are lines that only intersect one of the axes and not the other.

Originally posted by FabianFnas
Prove, that 1+2=3

Is this provable? Yes it is.
Most of math students, from lower grade of university, cannot. Can you?

1+2 is defined as 3 is it not?

Line may or maynot extend to infinity. It may be a small line. So circle with Infinite radius or similar figures dont hold good IMHO.

Originally posted by AThousandYoung
1+2 is defined as 3 is it not?

No, not more then 2+3=5, because you cannot define every combinations of a, b, and c so a+b=c.

Better to use the axioms and go from there.

However, addition is a defined operation, is it not?

Haha.
Wanna play chess?!

Originally posted by FabianFnas
No, not more then 2+3=5, because you cannot define every combinations of a, b, and c so a+b=c.

Better to use the axioms and go from there.

However, addition is a defined operation, is it not?

I would think yes more than 2+3=5, but not more than 1+3=4. 1+n gives you the number in the sequence that comes after n.