- #1
evinda
Gold Member
MHB
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Hi! (Smirk)
According to my lecture notes:
Constitution of integers
Equivalence relation $R$ on $\omega \times \omega$
For $\langle m,n \rangle \in \omega^2$ and $\langle k,l \rangle \in \omega^2$ we say that $\langle m,n \rangle R \langle k,l \rangle$ iff $m+l=n+k$.
First Step: $R$ is an equivalence relation.
Second step: We define $\mathbb{Z}=\omega^2 /_{ R}=\{ [\langle m, n \rangle]_{R}: m, n \in \omega\}$
Could you explain me why we can define the set of integers like that? (Thinking)
According to my lecture notes:
Constitution of integers
Equivalence relation $R$ on $\omega \times \omega$
For $\langle m,n \rangle \in \omega^2$ and $\langle k,l \rangle \in \omega^2$ we say that $\langle m,n \rangle R \langle k,l \rangle$ iff $m+l=n+k$.
First Step: $R$ is an equivalence relation.
Second step: We define $\mathbb{Z}=\omega^2 /_{ R}=\{ [\langle m, n \rangle]_{R}: m, n \in \omega\}$
Could you explain me why we can define the set of integers like that? (Thinking)