Thread: How intelligent do you think you are?

Originally Posted by no-Name

tommo's objective view on subjective riddles is very silly, by the way

What?

Originally Posted by Xei

If all x is... odd? The correct statement is 'for all x, if x is odd, etc.', but of course that is implicit in the 'if x is odd', and the 'for all x' is often omitted. To be really strict we should be saying 'for all positive integers x, etc.', but from the context of the discussion we already knew what we're talking about. But sure.

With respect to 'if it works enough then that is likely correct': well, that is the whole point of my post; that is, the problem of induction. The point is that 'yeah that's probably right' is not in any sense a proof. What is the basis for even thinking that, because the statement checks out for a few numbers, it'll check out for all of them? Take the (for these purposes very simplified) statement, 'x is less than 1,000,000,000,000,000'. You could work at that via your method of proof for a lifetime and be convinced that it is universally correct.

Sorry about that, early in the morning (hadn't slept yet lol) I realised that I wrote the wrong thing as I was going to sleep, but had to say fuck it.

Originally Posted by Xei

Now, the most interesting part of what you said. Bearing in mind that what we're trying to achieve is a proof of 'for all positive whole x, 0 + x = x': can you delineate exactly how your proof works? As it stands, it's running roughly as

x = x
hence
0 + x = x
(because the former is just 'the latter shortened')

but what is your basis of this being a valid inference? It seems to me that what you have done is added 0 to the left of both sides, and then, on the right, used the fact that 0 + x = x. But... that's what we are trying to prove in the first place, you can't use it as part of your proof.

You could add 0, or just take it out.
But you really see that all that statement says is x is x. Because 0 is nothing, so it's basically unneeded in the equation.
And of course x is x. It can't be anything else.

So I wasn't really using it as part of my proof. Well, I dunno maybe it is in a way.
But I really just used it to show that it is saying x=x. And proved that x=x by showing that one thing cannot be another thing.

As for the 'all x < 1000000000' thing.
This is similar to sorry if I've got this wrong, but I think:
There was the theory of mechanics which Newton proposed, but when you got to very small sizes, it didn't work, which is why Einstein came up with his Theory of Relativity.

So the same would most likely happen with this 'all x < 10000000000' thing.
If we only needed 1000000000 numbers.... this is illogical btw lol All numbers are less than 1000000000 (a number lol)
Oh well.
If we only needed that many, it would suit us fine, we would say it is correct that every number is under 100000000.
But if we suddenly needed to go over that number, we would find another rule, 'all x is > 0' or 'all x is < 1000000000000000000000000000000000000' if we weren't as smart.