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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]

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

"?"

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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