The only other distinction between == and =:= is for integers and floats. Integers are not =:= to the corresponding float, but are ==, so it has nothing to do with closeness.

-0.0 is a weird dumb no mathematical value that IEEE 754 put in (for example the standardized value for sqrt(-0.0) is not even justifiable based on their choices). I think they didn't want 1/(1/-Inf) to be Inf, or something.

In the end think of erlang's "==" as "equal in value" and "=:=" as "equal in representation in memory".

Now if you really want to raise the hackles of someone using Erlang, should ask why integers and floats don't have a well ordering, and what you should do when you sort them.

It is not about being very close. IEEE says "Comparisons shall ignore the sign of zero" and erlang (or rather CPU instructions erlang outputs for float == float) respects that

While =:= is not something mandated by IEEE. Erlang implements such an operator on floats and it decides to compare false for 0.0 & -0.0. So it compare bits/does integer comparisons on same data

Ah, so == is compliant, and =:= is extra. Makes sense!