So what are axioms? Axioms are true facts about math that we can intuitively understand, but if we had to prove them, it would be incredibly difficult to do so, involving equal signs and x’s all over the place.
The first one I’m going to mention in this post is called the distributive axiom. This summarizes the distributive property of multiplication: x (y + z) = xy + xz.
There is the associative axiom, which basically means that if you have multiple addition or subtraction operations, order doesn’t matter. (xz)y = (zy) x, and so forth.
The commutative axiom is very closely related to the associative axiom, and says this: The order of addition or multiplication doesn’t matter. x + y = y + x, and xy = yx. Pretty much identical to the associative property.
The transitive axiom of equality says that if x = z, and z = y, then x = y. The axiom after this is the symmetric axiom of equality. This menas that if x = y, then y = x. This also means that if x + 4 = y – 3, then y – 3 = x + 4.
The reflexive axiom is incredibly easy to understand. x = x. That’s all there is to it. A number equals itself. Kind of hard to actually prove that a number equals itself, no?
The addition and multiplication properties of equality> Something that you’ll end up using a lot in more complex algebra, this means that if x = y, then zx = zy, or z + x = z + y, etc.
The Blogger 
Leave a comment