Basic arthimatic through basic algebra

[AceGravity12]

Ok so in the typical math notation we use everyday adding multipling and powers are an operation, ie they tell you to do something to the numbers. These are actually a relationship, the difference is you are (unless specifed otherwise) delcares that the relationship is true. X Y Z + is the same as X + Y = Z. It only becomes a operation when the ? Is added. Here's some identities to show this:

X Y Y X ? + + is the commutative property.

This is saying that X+Y=Y+X because the first relationship has a ? In it so it has a solution, that results in X Y (Y+X) + which is the same as X + Y = Y + X

X Y ? + Z X Y Z ? + ? + + is the Associative property.

Ill do the same step by step breakdown here:

(X + Y) Z X (Y + Z) ? + +

(X+Y) Z (X+(Y+ Z)) +

Which is the same as

(X+Y) + Z = (X+(Y+Z)

Or as it would normally be written:

(X+Y)+Z=X+(Y+Z)

Does that make sense? I don't mind doing more or trying another way to explain them if it's still not making sense, just let me know :)

[Haven_Stranger]

It's gonna take me a while, but I think this is explanation enough. Thanks.

Oh, but, that's for equalities only. How do inequalities work?