Quote:
Originally Posted by Batalov
In a nutshell, he says:
Let's take a rational number p/q = 2/3.
"but definition of the odd/even has absolutely no sense for rational numbers," (direct quote)
so we cannot say that integer p=2 is an even number. it's neither even nor odd. It is 1.99999999999... End of proof.
Is that right, Evgeniy? 2 is not an even number? Would it make you feel better, if p/q = 1414/1000, "we cannot prove that integer 1414 is an even number"?
I attached his "proof".

Ã…ctually, no :) 2 is 2, but when you deal with rationals you cannot treat them like natural numbers. for example..
at 1st glance, looks strange, but...
according to the very principle of limits, approximation of continuous function cannot reach its final point. Here we could recall
Achilles and the Tortoise