- #1
symaticc
- 2
- 0
Homework Statement
I know how to prove that square root of 2 is irrational using the well ordering principle but what I'm wondering is, how can we use the well ordering principle to prove this when the square root of two isn't even a subset of the natural numbers? Doesn't the well ordering principle only hold for natural numbers and not rational numbers? If we prove that the well ordering principle does not hold for the square root of 2, aren't we just proving that the square root of 2 is not a natural number?
Thanks in advance!