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let-Z-N-0-f-Z-Z-Z-f-m-n-m-n-m-n-1-2-m-prove-that-f-is-a-one-to-one-function-and-also-an-onto-function-




Question Number 67055 by Tony Lin last updated on 22/Aug/19
let Z_+ =N∪{0}, f: Z_+ ×Z_+ →Z_+   f(m, n)=(((m+n)(m+n+1))/2)+m  prove that f is a one-to-one function  and also an onto function
$${let}\:\mathbb{Z}_{+} =\mathbb{N}\cup\left\{\mathrm{0}\right\},\:{f}:\:\mathbb{Z}_{+} ×\mathbb{Z}_{+} \rightarrow\mathbb{Z}_{+} \\ $$$${f}\left({m},\:{n}\right)=\frac{\left({m}+{n}\right)\left({m}+{n}+\mathrm{1}\right)}{\mathrm{2}}+{m} \\ $$$${prove}\:{that}\:{f}\:{is}\:{a}\:{one}-{to}-{one}\:{function} \\ $$$${and}\:{also}\:{an}\:{onto}\:{function} \\ $$

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