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## Main Question or Discussion Point

I need help understanding this proof. The textbooks says,

For every k∈{1,...,n} there exists an m

His justification for this, is that for every real number x there exists an natural number n such that n≥x.

I fail to see the connection between the two. Please help :(

For every k∈{1,...,n} there exists an m

_{k}∈ℕ such that (n choose k) r^{n-k}1/m_{k}^{k}< δ/nHis justification for this, is that for every real number x there exists an natural number n such that n≥x.

I fail to see the connection between the two. Please help :(