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Question: Is there any supremum and the infimum of the set

$$ \{x ∈ \mathbb{Q} \mid 1

my answer is $\sup= \sqrt 5$, $\inf=1$.

Am I right ?

So $\mathbb{Q}$ in this question doesn't matter?

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    This question is unclear. Do you mean "does there exist an infimum or supremum"? – 2017-02-27
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    $\inf = 1$ yes but $\sqrt{5} \notin \mathbb{Q}$, so the $\sup$ doesn't exist. – 2017-02-27
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    I and Henning made some edits to your post. Please try to follow them so you know how to format questions properly here. – 2017-02-27

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It matters whether you consider your set as a subset of the ordered set $(\mathbb Q,{\le})$ or the ordered set $(\mathbb R,{\le})$.

In the former case there is no supremum (because the supremum of a subset has to be an element of the ordered set you're considering); in the latter case $\sqrt 5$ is correct.

Lesson to learn: the terms "supremum" and "infimum" depends not only on what the set is, but also on what you consider it as a subset of.

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    but it doesn't matter '<' or ' ≤ ' , right ? – 2017-02-27
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    @Karry: Yeah, that is just a question of which convention you're using for specifying an ordered set. – 2017-02-27