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When mathematicians state:

  • "let $x$ be an arbitrary integer"
  • "let $x$ be any integer"
  • "let $x$ be an integer"

what do they actually mean?

I asked a very similar question here:

Question about how to interpret arbitrary elements

however, here I am not asking whether my interpretation is correct, but instead how most mathematicians actually think about these statements.

Thank you for your time.

Pranav Jain
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  • I don't think this needs to be a second question. You could just edit your previous question to clarify. – Jair Taylor Dec 19 '20 at 00:47
  • Do you program? How do you think about x in reverse_string(x: string): string? – Trevor Gunn Dec 19 '20 at 00:47
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    I sometimes say "Suppose that $x$ is an integer" instead of "Let $x$ be an integer." It means the same thing. Ok, so we know that $x$ is an integer, and that's all we know about $x$. By the way, I almost never use the word "arbitrary". – littleO Dec 19 '20 at 00:49
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    It means that whatever we are about to say regarding $x$ will be something that applies to all integers (since we have no other assumptions). – Nick Dec 19 '20 at 00:55
  • @TrevorGunn Yes I program (alot actually). The way I would think about $x$ when writing a reverse_string function is that it is the identifier to the memory location of my user's input (in this case, a string). – Pranav Jain Dec 19 '20 at 01:01

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