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diff --git a/Problem Set 2.page b/Problem Set 2.page index 7a14581..d65f293 100644 --- a/Problem Set 2.page +++ b/Problem Set 2.page @@ -43,5 +43,5 @@ $\int_0^{2\pi} |\sin^2(x)|^2 dx = \sum |a_n|^2.$ Cardinality of the natural numbers (countable): $\mathbf{N}$,$\mathbf{Z}$ Cardinality of the real numbers (continuum): $\mathbf{R}$ -Proofs: +Proofs: - $\mathbf{Z}=\mathbf{N}$ under the bijection $n \mapsto 2n+1$ for nonnegative $n$ and $n \mapsto 2|n|$ for negative $n$. For example, ${-2,-1,0,1,2} \mapsto {4,2,1,3,5}$.
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