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An irrational number is a real number that cannot be expressed in the form $\frac{n}{m}$ where $n$ and $m$ are integers.
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votes
Compilation of strategies to show that some constant is irrational
The original and some subsequent proofs of the irrationality of $\pi$ implicitly use the following lemma:
If there is a sequence $P_n(x) \in \mathbb{Z}[x]$ such that $P_n(\alpha)>0$ and $P_n(\alpha)=o …