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RTXEnabledViera t1_ja1vdl1 wrote

= is used to signify two numerical quantities are equal. 5=6-1.

≡ is used in lieu of "is the same as", verbally speaking. It denotes identities, i.e. two expressions whose value is equal no matter what the variables are. For example: (a+b)^2 ≡ a^2 + 2ab + b^2 . In most cases, we simply use = instead, but it is important to remember that it's simply an equivalence sign.

Do note that ≡ is more frequently used to denote congruence. Two numbers are congruent modulo a number N if N divides their difference. We write a ≡ b (mod n).

⇔ is "if and only if". P ⇔ Q means Q is true if and only if P is true. The truth table for this condition is such that P ⇔ Q is true in two cases: both P and Q are true, or both P and Q are false. This logical equivalence can also be written, albeit less frequently, as P ≡ Q

↔ is used exactly the same way as ⇔. No difference whatsoever.

Summary: It's better to learn these symbols as part of the required reading, there sometimes is significant overlap between what they are used for.

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