More Mathematical Logic

Axioms of equality are basic rules for using the equals sign…

The Additive Axiom Of Equality:

If a=b and c=d, then a+c=b+d.

The Additive Axiom Of Inequality:

If a>b, then a+c>b+c.

Identity Element For Addition:

Any number added to 0 gives the original number, for instance, n+0=n.

Identity Element For Multiplication:

Any number multiplied by 1 gives the original number, for instance, n*1=n.

Multiplicative Axiom Of Equality:

If a=b and c=d, then ac=bd.

Negative Multiplication Property Of Inequality:

You must reverse the inequality sign when multiplying or dividing by a negative number.

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