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Question Number 68947 by Cmr 237 last updated on 20/Oct/19
$$\mathrm{please} \\ $$$$\mathrm{utilise}\:\mathrm{cette}\:\mathrm{fonction}\:\mathrm{to}\: \\ $$$$\mathrm{sh}\boldsymbol{\mathrm{ow}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{N}}\ast\boldsymbol{\mathrm{N}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{denombrable}} \\ $$$$\:\mathrm{f}:\boldsymbol{\mathrm{N}}\circledast\boldsymbol{\mathrm{N}}\rightarrow\boldsymbol{\mathrm{N}} \\ $$$$\:\:\:\:\left(\mathrm{x},\mathrm{y}\right)\shortmid\rightarrow\frac{\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}+\mathrm{y}+\mathrm{1}\right)}{\mathrm{2}}+\mathrm{y} \\ $$$$\mathrm{montrer}\:\mathrm{que}\:\mathrm{f}\:\mathrm{est}\:\mathrm{bijective} \\ $$$$\:\:\:\boldsymbol{\mathrm{P}}\mathrm{lease}\:\mathrm{help} \\ $$$$ \\ $$$$\:\:\:\:\:\: \\ $$