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3
votes
0answers
115 views
Direct proof that $\sqrt{2}$ is irrational? [duplicate]
Possible Duplicate:
Irrationality proofs not by contradiction
I've been puzzled for some days now, and I can't come up with an answer.
I'm trying to come with a direct proof that $\sqrt{2}$ ...
5
votes
3answers
387 views
Is this proof that $\sqrt 2$ is irrational correct?
Suppose $\sqrt 2$ were rational. Then we would have integers $a$ and $b$ with $\sqrt 2 = \frac ab$ and $a$ and $b$ relatively prime.
Since $\gcd(a,b)=1$, we have $\gcd(a^2, b^2)=1$, and the fraction ...
5
votes
1answer
906 views
Sum of irrational numbers
Well, in this question it is said that $\sqrt[100]{\sqrt3 + \sqrt2} + \sqrt[100]{\sqrt3 - \sqrt2}$, and the owner asks for "alternative proofs" which do not use rational root theorem. I wrote an ...
1
vote
3answers
269 views
How to prove $e$ isn't a $\frac {a}{b}$. Not irrationality with other ways or about transcendental, only about fractions
I would like a proof that $e$ isn't a fraction $\frac{a}{b}$, for $a,b \in Z$ and $mdc(a,b)=1$.
Just a observation =) I'd like a proof with fractions, not about $e$ irrationality or if $e$ is ...
