For instance if I’ve to prove a math theorem on some particular number, I may not actually need to know the number (in the sense of directly writing it out on paper), I just need to know some useful properties of the number which I can use for the proof. I can just assume it is N, and say N has some properties and move on.
Don’t forget to prove that some such number exists! I can’t remember the details[1], but IIRC there was an entire branch of math based around a class of objects that, it turns out, doesn’t actually exist[2].
(Edit: it appears to be apocryphal. See my reply to acylhalide below.
Don’t forget to prove that some such number exists!
I can’t remember the details[1], but IIRC there was an entire branch of math based around a class of objects that, it turns out, doesn’t actually exist[2].(Edit: it appears to be apocryphal. See my reply to acylhalide below.
And it may be an apocryphal story
As in, a vacuous / empty set.
I looked it up, and it appears to be apocryphal.
There are specific instances of it occurring to a single person, but nothing as widespread as a branch of math.