1/5
just the field axioms idk. Most apply specifically to real numbers but I didn't add that.
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closure
Numbers are closed under multiplication and addition (xy=real)
commutativity
Mult and Add are commutable operations. Order does not change value. (xy=yx)
associativity
Mult and Add are associative operations. Parenthesis does not change value (xy)z = x(yz)
distributivity
Multiplication distributes over addition
Identity
Multiply 1 or adding 0 does not change value
Inverses
Every number has the additive and multiplicative inverses -x and 1/x