Thread: How intelligent do you think you are?

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.

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.