"Equivalence" is used in business, that is, the value of different commodities is equal. For example, "equivalent exchange" means exchanging different commodities with equivalent value.

In mathematics, "equivalence" is not equal, and equivalence is not necessarily equal.

Solving equations, solving inequalities and proving some propositions are all equivalent transformations of utilization. For example:

Equation x+8= 1 and 2x+ 16=2 are equivalent;

Inequalities x > 5 and–2x