# Question about supremum and infimum

Say we have $a = \sup \{ a_{1}, a_{2}, a_{3}, ... \}$. Then does this mean we can find some $a_{n} \in \{ a_{1}, a_{2}, ... \}$ such that

$$|a - a_{n}| < \varepsilon$$

? My reasoning is that since a (the supremum) is the least upper bound of the set, we have to be able to find some member of the set that is arbitrarily close to a otherwise a wouldn't be a supremum anymore. Is this true?

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