Let's go.........RANDOM!

[Xocrates]

Well, now I'm sad.

From all the examples, the one was asked to do was the stupid cats and dogs one

[Feud]

We did oral arguments on cats v. dogs a few months back, it was fun.

[xander]

Proposition: There are no uninteresting positive integers.

Proof: Suppose for contradiction that there are uninteresting positive integers. The set of uninteresting positive integers must have a least element. The property of being the smallest uninteresting positive integer is interesting, which is a contradiction. Therefore there are no uninteresting positive integers. QED

xander

[NeatNit]

I find 428 pretty uninteresting.

Though interestingly, how come I chose 428 speciOH MY GOD

[trickser]

[xander]

I find 428 pretty uninteresting.

Though interestingly, how come I chose 428 speciOH MY GOD

Speaker: I have a remarkable proof of the statement.

Audience Member: But I have found a counterexample.

Speaker: It doesn't matter, I have another proof!

xander

[NeatNit]

Really though, all you created was a paradox. By declaring an integer interesting based only on how it's actually uninteresting, you took away the one thing that made it interesting. Since interesting-ness is not self-supporting, it jumps back to being uninteresting, hence the paradox.

[Xocrates]

Though one can note that there will be one or more numbers which possess the least amount of interest.

[trickser]

the least amount of interest.

If there is a least amount of interest, then interest is a value, in contrast to being just a property. If it is a value, then you can sort by the value. If you can sort by value of interest and sort by the nominal value, then you are not talking about integers.

[Xocrates]

then you are not talking about integers.

Why not? It's a property in the same sense that the number of digits of a number is a property of that number. Having a secondary numeric value associated to a number doesn't change the value of that number.

[xander]

Really though, all you created was a paradox. By declaring an integer interesting based only on how it's actually uninteresting, you took away the one thing that made it interesting. Since interesting-ness is not self-supporting, it jumps back to being uninteresting, hence the paradox.

Proofs 101, NeatNit. I assumed that there were uninteresting numbers. If you make that assumption, you come to a contradiction (what you are calling a paradox). Since the assumption led to a contradiction, the assumption must have been wrong. The assumption was that there were uninteresting positive integers, hence I have shown that there are no uninteresting positive integers. The problem is not the structure of the proof. Rather, if you are going to claim that there is a problem, it will be in the formal definition of "interesting."

xander

[trickser]

then you are not talking about integers.

Why not? It's a property in the same sense that the number of digits of a number is a property of that number. Having a secondary numeric value associated to a number doesn't change the value of that number.

The number of digits is a deduced property, it depends on the numbers (we talk about integers, right?) value and some arbitrary rule to express it. The introduced property of interest is independent of the numbers value. Thats a difference.

That will change the numbers from a one dimensional field to a tow dimensional field, when the definition of integers is probably something about 1 and its successors. But arguing with the definition seems cheap (and silly when you don't actually know it), but I suspect some change in capacity to be found.


lets say you have 1 with interest -1 and 2 with interest 2

so 1+1 is 2 but interest is -2, so 1+1!=2

[Xocrates]

That's actually bullshit in more ways than one

Even assuming that the interest property is not independent per integer, we have not established how the + operator works in regards to interest. That your result is incorrect is enterily hipothetical.

Also:

The introduced property of interest is independent of the numbers value.

No it's not. Whatever interest the number has, will be directly or indirectly tied to their value.

For instances, 1 may be interesting partly because it's the lowest odd number, but you need to know its value to determine that.

[xander]

That will change the numbers from a one dimensional field to a tow dimensional field, when the definition of integers is probably something about 1 and its successors.

The integers, let alone the positive integers, do not form a field---the integers are not closed under multiplicative inverses (and the positive integers are not even closed under additive inverses).

xander

[Ace Rimmer]

So then, no positive integer is uninteresting?

Great. Moving on to more important subjects; aliens and bigfoot are real. See all the proof!