I'm an AP Calc BC student. We just learned Euler's way to prove the irrationality of e. I just suddenly came up with this weird proof in class. But I couldn't find anything wrong with it. Can you guys check this proof and point out any mistake hopefully? Thanks a lot!
if e is rational, then e=m/n(simplest form), where m,n are unequal integers(n is not 0)
then ln(e)=ln(m/n)
then 1=ln(m/n)=logn(m)
that turns out m=n, which is not true and also contradicted to "m,n are unequal integers"
then e is irrational.
if e is rational, then e=m/n(simplest form), where m,n are unequal integers(n is not 0)
then ln(e)=ln(m/n)
then 1=ln(m/n)=logn(m)
that turns out m=n, which is not true and also contradicted to "m,n are unequal integers"
then e is irrational.