One Question about Proof on Irrationality of e
I'm looking at this particular proof that is irrational. Please find it beneath my writing.
This proof by contradiction assumes that . I understand this.
However, while proving that is the contradiction, the proof uses the second boxed inequality
and so on...
However, although , it is entirely possible for AND since .
In this case then the , so the above steps and the proof itself fail?
Thank you very much for your assistance.
Re: One Question about Proof on Irrationality of e
It should be pretty obvious that q is a positive integer, because of how q is defined in a and b.
Originally Posted by scherz0
And since the proof involves showing that e = p/q, and it can easily be seen that e > 0, since q > 0, then so must be p.