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What does the notation $11|a^2$ mean as used in this answer: https://math.stackexchange.com/a/948251/13230

I am trying to understand the proof that $\sqrt{11}$ is an irrational number, but am stuck when the following is stated:

This means that $11|a^2$ and so $11| a$ as $11$ is prime.

Steeven
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  • It means "$11$ is a divisor of $a^2$". – 5xum Sep 02 '15 at 21:35
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    Why didn't you comment in the question you mention?

    It means that $11$ divides $a^2$.

     – Silvia Ghinassi Sep 02 '15 at 21:35
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    $a|b$ if and only if there is some integer $k$ for which $b=k\cdot a$. So, $2|4$ or $11|121$. – 5xum Sep 02 '15 at 21:36
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    @SilviaGhinassi It would actually be considered bad form and most likely ineffective to comment on that post. For one thing, the answer in question was written years ago and by a user who has not returned. No one will read the comment. Secondly, this is a disjoint question from before and is unrelated to the original topic of proving the irrationality of $\sqrt {11} $. Thus, it should be a separate question. While this might be a duplicate (but I'm on my phone right now so it's hard to check), it should not have been a comment. That's not what comments are for. – apnorton Sep 03 '15 at 13:33
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    @apnorton I really like how constructive your comment is. I'll keep this in min in the future! – Silvia Ghinassi Sep 03 '15 at 14:02

1 Answers1

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The notation means that "$11$ divides $a^2$." In other words it means there exists an integer $n$ such that $11n=a^2$.

Peter Woolfitt
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    Why are we answering question that are "bad" or shouldn't even be questions? – Silvia Ghinassi Sep 02 '15 at 21:37
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    @SilviaGhinassi I consider this a perfectly reasonable question about notation. Just because it's common doesn't mean everyone knows it. – Peter Woolfitt Sep 02 '15 at 21:38
  • This question should be a comment elsewhere (note that OP has enough reputation). – Silvia Ghinassi Sep 02 '15 at 21:38
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    @SilviaGhinassi I agree that it could be a comment, but not that it necessarily should be a comment. The question "what does the notation $a\mid b$ mean?" can be stand alone. – Peter Woolfitt Sep 02 '15 at 21:40
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    @SilviaGhinassi By the way, I did read and support your meta post. It just seems we have different criteria for 'bad questions.' – Peter Woolfitt Sep 02 '15 at 21:51
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    @SilviaGhinassi comments are second class citizens. The sysadmin of SE always puts his mug of coffee on the floppy drive they are stored on. They'd be gone if it tips over. But that's ok, because it's a Q&A site, not a Q&A&C site. Isn't it the case that in the field of mathematics techniques used to do one thing come out to be surprisingly interesting or useful for another? And isn't a bunch of new questions a possibly more rewarding result than the answer to the original question that they are derived from? – null Sep 02 '15 at 21:51
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    The fact that there are 4000+ questions with the (notation) tag implies to me that it is a valid question. – shoover Sep 02 '15 at 22:16