Is one of the following more correct than the other, or does it simply not matter?

$i = \sqrt{-1} \quad$ or $\quad i := \sqrt{-1}$?

Here I am using $:=$ to mean "defined to be equal to."

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    $\begingroup$ I wouldn’t write either. $\endgroup$ – Randall Nov 28 '18 at 12:28
  • $\begingroup$ @Randall okay, what could you write instead? $\endgroup$ – Gurjinder Nov 28 '18 at 12:32
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    $\begingroup$ @Randall Do you mind expanding on this comment? Otherwise is not very useful for the OP $\endgroup$ – caverac Nov 28 '18 at 12:32
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    $\begingroup$ $i^2=-1$........ $\endgroup$ – Randall Nov 28 '18 at 12:32
  • $\begingroup$ @caverac You are correct. Fair point. $\endgroup$ – Randall Nov 28 '18 at 12:33

None of them are correct as the square root is not a single-valued function. The best expression (i.e. simplest) defining $i$ would be $i^2=-1$.

  • $\begingroup$ Okay fair enough. Why not $i^2 := -1$? $\endgroup$ – Gurjinder Nov 28 '18 at 12:37
  • $\begingroup$ Okay, I think the OP had an error. Let's think about $i$ as $\pm\sqrt{-1}$. $i=\pm\sqrt{-1}$ or $i:=\pm\sqrt{-1}$? $\endgroup$ – manooooh Nov 28 '18 at 12:39
  • $\begingroup$ You can write that. $:=$ is usually used in definitions. Since $i$ is widely used, we don't need to "define" it everytime. Also, that notation is hardly ever used. But if you want, no one is stopping you (possibly once in a discussion/problem). $\endgroup$ – SinTan1729 Nov 28 '18 at 12:39
  • $\begingroup$ @manooooh Okay, thank you for the clarification. $\endgroup$ – Gurjinder Nov 28 '18 at 12:44
  • $\begingroup$ @SinTan1729 Okay, thank you for the clarification. $\endgroup$ – Gurjinder Nov 28 '18 at 12:45

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