View Single Post
2021-01-03, 23:16   #72
SarK0Y

Jan 2010

5616 Posts

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".
Åctually, no :) 2 is 2, but when you deal with rationals you cannot treat them like natural numbers. for example..
$\frac{1}{9}\cdot9 \neq\frac{9}{9}\cdot1$
at 1st glance, looks strange, but...
$\frac{1}{9}\cdot9 \eq0.11111111111111..11\cdot9$

according to the very principle of limits, approximation of continuous function cannot reach its final point. Here we could recall
Achilles and the Tortoise