Although in Erlang it's closer to an equation with assignment being a side effect. `=` is the pattern matching operator.

    Eshell V15.2.6 (press Ctrl+G to abort, type help(). for help)
    1> X = 1.
    1
    2> X = X.
    1
    3> 1 = X.
    1
    4> X = 2.
    ** exception error: no match of right hand side value 2
    5>

That's exactly right. Looking at the Assignment Operator Wiki page, it's also clear where these notations come from.

I think an easy way to look at it, for someone coming from a math background, is to think of programming lines as instructions, instead of statements. x=x+1 can be then read as "let x be x+1", and that's it.

https://en.wikipedia.org/wiki/Assignment_(computer_science)

It’s not really such a different meaning, it’s just shorthand for something like:

    X’ = X + 1
    DELETE X
    X = X’

Even if you treat it as “storing a value in a slot”, a comprehensive model of the operation needs to model the fact that the value of the slot changes over time. So another way to look at it would be:

    X_t1 = X_t0 + 1

…except that “X” is shorthand for “the latest binding that uses this name.”