What are the axioms of similarity?

A theorem is a proved rule but an axiom cannot be proven but is stated to be true.

axioms are statements which cannot be proved.but these statements are accepted universally.we know that any line can be drawn joining any two points.this does not have a proof

An axiom is a self-evident truth that is not proven, only accepted, such as that for any two real numbers a and b, either a > b, a = b, or a < b.

Commutative Property: The order of the objects from left to right doesn't matter. For example : 5+3+2 = 3+2+5 = 2+3+5, etc... Because addition is commutative.Associative Property: Where we put...

Say there's a relation ~ between the two objects a and b such that a ~ b. We call ~ an equivalence relation if: i) a ~ a.ii) If a ~ b. then b ~ a.iii) If a ~ b and b ~ c, then a ~ c. Where c is...