Here is another proving blog, this time doing why the square root of 2 is an irrational number by using contradiction. Which is basically stating that if the statement is true then that mean... and by doing so you show the statement is false.
Anyway here is my working out. If you see any errors let me know immediately, I’m prone to making them.
Comments (5)
a and b are integers, not strictly natural numbers, where b does not equal zero and a and b have no common factors. k is also an element of the integers, not just naturals. And at the end I think you used the wrong symbol. We usually use a capital Q to represent the rationals, while a capital R represents the reals.
Yeah I mixed real and rationals
I purposely used naturals numbers so that I can use positive integers. You can easily achieve the same results using and positive or negative integer
Two things:
1. The fact that a and b are coprime doesn't imply that one is even and the other odd. For example, 3 and 25 are coprime, but they're both odd.
2. Why did you sub in k+1 for b? The rest of your logic, starting from that point just falls apart.
Thanks for the help! I hope the newer version is better explained