All integers are interesting

[aryobarzan]

Let's prove this by contradiction. Suppose there exists at least one integer which is not interesting. Among all non-interesting integers we take the least, Then it must be interesting , since being the smallest non-interesting integer is an interesting fact! We came to a contradiction, So all integers all interesting

[theboss]

Lol nice one
but how about the other numbers? D:

[aryobarzan]

Well we can do the same with rational numbers since they are countable.

[theboss]

How about the irrationals?

Also the img tags don't support .svg, so here's the link for the rest of ya.
http://upload.wikimedia.org/wikipedia/c ... gument.svg

[Zapp]

irrationals? try finding their last digits, it will be an interesting journey

[xander]

The original proof works in the natural numbers (or positive integers), but it fails on the integers. It fails to take into account that the set of uninteresting integers may not have a least (or greatest) element. As the integers are unbounded both above and below, the existence of a least (or greatest) element is by no means certain. As I originally heard the joke, it relies upon the fact that the natural numbers are bounded below, hence there must be a lower bound for the set of uninteresting numbers.

The same argument applies to the rationals, the irrationals, and the reals. Even more so to the complex numbers, which are not strictly ordered.

xander

[aryobarzan]

Well, You can first prove that all non-negative integers are interesting, then prove that all negatives are.

[E_net4]

It's true, apparently. We would need to make sure the lowest of the integers was interesting.
What bothers me most is the recursion in there. If the lowest of the uninteresting numbers becomes interesting, we can't reapply the theory to get the next one, even though it is considered interesting. Like, how can A be interesting just because it's the second smallest uninteresting number? But I guess we need a plausible definition of an interesting number first.

[malt16]

It's true, apparently. We would need to make sure the lowest of the integers was interesting.
What bothers me most is the recursion in there. If the lowest of the uninteresting numbers becomes interesting, we can't reapply the theory to get the next one, even though it is considered interesting. Like, how can A be interesting just because it's the second smallest uninteresting number? But I guess we need a plausible definition of an interesting number first.

But A wouldn't be the second smallest uninteresting number, because A-1 is now interesting. So A would be the new smallest uninteresting number, thus making it interesting.

[aryobarzan]

It's true, apparently. We would need to make sure the lowest of the integers was interesting.
What bothers me most is the recursion in there. If the lowest of the uninteresting numbers becomes interesting, we can't reapply the theory to get the next one, even though it is considered interesting. Like, how can A be interesting just because it's the second smallest uninteresting number? But I guess we need a plausible definition of an interesting number first.

Well we don't really need to prove that all non-interesting integers are interesting.
I want to show that the set of non-interesting integers is empty. So the so called 'Second non-interesting' integer doesn't exist at all. Because we even don't have the first non-interesting

Spoiler! :

Sorry if I didn't explain well

Spoiler! :

Of course we need a plausible definition for what we call 'interesting' , that's why i put this topic in jokes

[E_net4]

Ha HA! I killed your joke with the attempt of serious resolution methods!

[xander]

Ha HA! I killed your joke with the attempt of serious resolution methods!

Isn't that what most math people do? Analyze jokes to death?

xander

[gwtkof]

All reals are interesting.

Consider that if an argument shows that all reals are interesting then it itself is interesting, and any real number used in the proof is by extension interesting, as well (since it was used in an interesting proof). (1)
So let x be real. Clearly x is featured in this proof and this proof is interesting so by (1) x is interesting. But x was arbitrary, therefore all reals are interesting.

QED