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I found the definition. If S is supremum of set A, then

a) [tex]\forall x\in A:x\leq S[/tex]

b) [tex]\forall\varepsilon>0\;\exists x_0\in A:S-\varepsilon<x_0[/tex]

Now let define set [tex]A=\{1,2,3,4,5\}[/tex]. Is number 5 supremum of set A? Condition a) is satisfied, but b) is problem. If [tex]\varepsilon=0.1[/tex], there isn't x_0 in the set A such that

[tex]5-0.1<x_0[/tex]

Could you explain that?

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# If S is supremum of set A

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