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Que.) $\{x ∈ :( \;, y)≤ r\}$ defined in metric space is known as ___________ ball.

Hey guys, i had given an exam recently and this was the question i have to attempt.... I know this question answer, but I want to know only that "is this question format correct or not ?" means in this question there is blank space on left side of coma of '$y$' . Is this standard representation for metric space or is this a wrong format?

Please help me out if this is wrongly formatted then it can save my 1 mark in exam.

Daniel
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Drasto
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    Welcome to MSE. We usually recommend formatting with MathJax. To answer your question, I suppose people have their own notation but I have never seen that. – Daniel Sep 10 '21 at 04:15
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    For one thing, inside the set bracket is a membership symbol just sitting there, not between any two things like usual in $x \in A$ [I mean it has a $\in$ symbol with nothing immediately to its right.] – coffeemath Sep 10 '21 at 04:18
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    @coffeemath thanks for answering.....you want to say question format is not correct. Am i right? – Drasto Sep 10 '21 at 04:46
  • It's not standard notation in set theory nor metric-space theory and I dk what it means but on a test I would guess "closed ball". – DanielWainfleet Sep 10 '21 at 05:31
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    Other things I would be missing: a) a definition what $y$ might be (is it a member of the metric space? b) the inequality seems to be meaningless. Maybe if $d$ is the metric then this inequality is intended to express $d(x,y) \leq r$ but a candidate should not be judged on his ability to autocomplete the question. – Maksim Sep 10 '21 at 08:34
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    @DanielWainfleet Thanks for solving my doubt, i understood what you want to say, and yes its answer is "Closed Ball". – Drasto Sep 10 '21 at 10:25
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    @Maksim Thanks for explaining all things clearly, you solved my doubt. – Drasto Sep 10 '21 at 10:26

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