assume the contrary
2 = p2
both sides by q2
must be even, for it is equal twice the value of an integer. ( q2
is therefore even
as well, for if the square of a number is even, the number is as well.
is even, it can be written as 2m, where m is some other whole number
. placed into the equation, it reads:
divide both sides by 2.
with the same arguments used previously, q must also be even, and may be represented as 2n. same steps, resulting in
lose the 2s.
can continue indefinitely, meaning the fraction is infinitely
reducable. A quality of a fraction is that it may be represented as a ratio between two relatively prime
integers. (like 10/20 can be reduced to 5/10, and finally to 1/2)