Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 198939 by Mingma last updated on 26/Oct/23

Answered by witcher3 last updated on 26/Oct/23

$$\phi :2\mathbb{N}\to \mathbb{Z}$$$$\phi \left(2\mathrm{n}\right)=\{\begin{array}{l}\mathrm{k}\mathrm{if}\mathrm{n}=2(2\mathrm{k}+1)\\ -\mathrm{k}\mathrm{if}\mathrm{n}=2.\left(2\mathrm{k}\right)\end{array}$$$$\phi \left(\mathrm{m}\right)=\phi \left(\mathrm{n}\right)\iff \mathrm{m}=\mathrm{n}$$$$\phi \mathrm{injective}$$$$\mathrm{if}\mathrm{n}\in \mathbb{Z}\mathrm{if}\mathrm{n}⩾0$$$$\mathrm{n}=\phi \left(2(2\mathrm{n}+1)\right)$$$$-\mathrm{n}=\phi (2.2\mathrm{n})$$$$\phi \mathrm{surjective}$$$$\mathrm{injective}\mathrm{surjective}?\iff \mathrm{bijection}$$$$\Rightarrow 2\mathbb{N}\approx \mathbb{Z}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com