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My professors have seemed to use $≅$ and $≈$ pretty interchangeably to indicate that something is nearly equal to something else, and I just became aware of $≃$.

When should we use one of these instead of the other? And, maybe more illustratively, when should one of them not be used?

Lucas
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    Context is important. In applied math, $\cong$ it denotes approximately; in Algebra, it denotes isomorphism; in geometry, it denotes congruence... – Weaam Jun 29 '17 at 02:07
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    Lets add some more.... $\sim$ is "similar to" but it can also appears in equivalence relations. I suppose similarity is an equivalence relation. $\equiv$ is "equivalent to" and appears in regularly in modular arithmetic. $\approx$ is aproximately. $\cong$ is congruence or isomorphism. And of course $=$ is equality. – Doug M Jun 29 '17 at 02:14
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    Ask your professors. Their use is idiomatic and you want to learn their idioms. – Matthew Leingang Jun 29 '17 at 02:23
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    And $\simeq$ denotes homotopic or homotopy equivalent. – anon Jun 29 '17 at 02:37
  • Duplicate of https://math.stackexchange.com/q/864606 – Tim Moore May 13 '24 at 06:19

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