What is an equivalent set?

Answer 1

In a chemical synthesis, an "equivalent" means a corresponding and equal amount of something. Usually, it is in terms of moles. For instance, if my reaction is A + B --> C, and I add 1 mole of "A" to my flask, then I would add one equivalent of "B" (or 1 mole of "B") because of the one-to-one stoichiometry. If the reaction was instead A + 2B --> C, then I would add two equivalents of "B" for each mole of "A" I used. This can be contrasted with the term "an excess" where for my first reaction above, I might add 1.5 moles of "B" for every mole of "A" so that there is always excess "B" in the reaction flask.

Answer 2

Two sets are said to be equivalent (not equevalent) if their cardinality is the same even if their elements are not the same. For finite sets this means that the two sets have the same number of elements. For infinite sets they must have the same order of infinity.

Equivalent infinite sets can do your head in. For example, the set of even integers is clearly a proper subset of the set of all integers. However, the mapping x -> 2x (where x is an integer) is equally clearly a one-to-one mapping between the two sets. This mapping shows that they have the same number of elements: this number is Aleph-null.