Cratylus
Junior Member
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- Aug 14, 2020
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- 82
I am using A book of set theory by Pinter
This is Ex:4.3.4
SupposeB⊆A;
prove that it if B has sup b then
,λ(v(B))∩v(B)={b}.
Proof
Let b=supB
v(B)={a∈A:a>x:[MATH]\in[/MATH] B }
and λ(v(B))={a∈A:a[MATH]\geq[/math]x where x[math]\geq{y} \; \forall \; y \in B[/MATH] }
Taking the intersection produces the result
Help
This is Ex:4.3.4
SupposeB⊆A;
prove that it if B has sup b then
,λ(v(B))∩v(B)={b}.
Proof
Let b=supB
v(B)={a∈A:a>x:[MATH]\in[/MATH] B }
and λ(v(B))={a∈A:a[MATH]\geq[/math]x where x[math]\geq{y} \; \forall \; y \in B[/MATH] }
Taking the intersection produces the result
Help