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roam
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Let [tex]l \in R[/tex] be the least upper bound of a nonempty set S of real numbers.
Show that for every [tex]\epsilon < 0[/tex] there is an [tex]x \in S[/tex] such that
[tex]x > l - \epsilon[/tex]
I don't understand this question very well, I appreciate it if you could give me some hints.
l is the l.u.b on S, therefore it is greater than or equal to any [tex]s \in S[/tex]
By the definition of the limit; |f(x)-l| < ε if 0 < |x-a| < δ
l-ε < x < l+ε
|f(x)-l| < ε
"?"
Show that for every [tex]\epsilon < 0[/tex] there is an [tex]x \in S[/tex] such that
[tex]x > l - \epsilon[/tex]
I don't understand this question very well, I appreciate it if you could give me some hints.
l is the l.u.b on S, therefore it is greater than or equal to any [tex]s \in S[/tex]
By the definition of the limit; |f(x)-l| < ε if 0 < |x-a| < δ
l-ε < x < l+ε
|f(x)-l| < ε
"?"
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