Notation is invented to be useful. A lot of mathematicians and physicists write stuff like
f = g + O(h)
and then proceed to do a bunch of manipulations without getting bogged down in set theory syntax.
Also equality isnt just defined on sets, usually people start by defining it as like a formal thing satisfying a bunch of rules as a part of their logic, and going from there.
Notation is invented to be useful. A lot of mathematicians and physicists write stuff like
f = g + O(h)
and then proceed to do a bunch of manipulations without getting bogged down in set theory syntax.
Also equality isnt just defined on sets, usually people start by defining it as like a formal thing satisfying a bunch of rules as a part of their logic, and going from there.