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No. Equality is defined on sets, with exactly one exception, this stupid fucking notation.
by mathgradthrow 7mo ago
No. Equality is defined on sets, with exactly one exception, this stupid fucking notation.
- foxes 7mo agoNotation 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.
- mathgradthrow 7mo agoEquality is defined on sets. Everything is a set. Equality means equalty as sets. That's how math aorks unless you're doing type theory shit.