What is the difference between equality and equivalence?

Question

I\'ve read a few instances in reading mathematics and computer science that use the equivalence symbol ≡, (basically an \'=\' with three lines)

Answer 1

I take your question to be about math notation rather than programming. The triple equal sign you refer to can be written ≡ in HTML or \equiv in LaTeX.

a ≡ b most commonly means "a is defined to be b" or "let a be equal to b".

So 2+2=4 but φ ≡ (1+sqrt(5))/2.

Here's a handy equivalence table:

Mathematicians      Computer scientists
--------------      -------------------
      =                      ==
      ≡                      =

(The other answers about equivalence relations are correct too but I don't think those are as common. There's also a ≡ b (mod m) which is pronounced "a is congruent to b, mod m" and in programmer parlance would be expressed as mod(a,m) == mod(b,m). In other words, a and b are equal after mod'ing by m.)