Irrational Definition and 355 Threads

Looking for "Easy" proof of Pi Irrational Hi, I just got to this forum after searching for an easy proof that Pi is irrational. The thread I found (google) was this one HERE. I wanted to reply, but since it is now “archived” I thought it would be better to post a new thread. Sorry if this...

Prove that sqrt2 + sqrt6 is irrational. Where do I start with this?

Does anyone on this forum believe reality should not be answered on an individual by individual basis? For indeed, we were all brought up under a diversity of circumstances, the very diversity which allows life to exist, and makes each one of us individuals. So who's to say one person is...

Here's the question that I got stuck: [inte]sqrt[x/(a-x)] dx .........(*) I tried to use the following substitution u=sqrt[x/(a-x)] and ........(1) dx = 2u(1-a)/(1+u2)2 du...(2) sub (1) and (2) into (*), after a few steps, I got (2-2a)[inte]du/(1+u2) - 2(1-a)[inte]du/(u2+1)2 The...

we know e (exponential) is a irrational number... how can we prove it??