Overloaded equal sign = and the word is

[Alain De Vos]

Problem,the equal symbol "=" in math is overloaded , as is the word "is" in language.
Is there a list of all the meanings of = in math and the word is.
For instance "is" can mean equal to , or element of a set.
Are there generally accepted alternatives to the "=" sign, so one can be more specific.
For instance := for equal per definition.

 

[disregardthat]

Why is it a problem that it's used extensively? As long as there is no ambiguity revolving around its use, I don't see how it could be a problem.

 

[Dr. Seafood]

Notation is simply about communicating ideas. So in an expression like 2 + 3 = 5, it's pretty clear what "=" denotes. When talking about isomorphism, congruence or some other type of "equality", :=, ≡, ⇔, ≈, etc. are used accordingly.

I find there's no need to be more specific. Mathematics is perfectly scrutinizing as it is (I don't mean that in a bad way). These are just symbols; a good math paper would be sure that there's no ambiguity in notation.

By the way, you wouldn't say "x is S" to mean x ∈ S, right? You would say "x is in S".

 

[SteveL27]

Problem,the equal symbol "=" in math is overloaded , as is the word "is" in language.
Is there a list of all the meanings of = in math and the word is.
For instance "is" can mean equal to , or element of a set.
Are there generally accepted alternatives to the "=" sign, so one can be more specific.
For instance := for equal per definition.

Actually, = is never overloaded in math.

It's an assignment operator in some programming languages; but every language that uses = for assignment uses == for equality, so there's confusion sometimes, but never overloading within a programming language or within math.

In typeset math they use \equiv for mod equivalence, and \cong for isomorphism. They never use = for anything but equality, as far as I know. Of course I could be wrong ... but I really don't think there are many alternate meanings or usage of = in math.

I think the main area where = is overloaded is in writing ASCII math, since there aren't any symbols for congruence, isomorphism, etc.