I shall use the word multitude to denote that character of a collection by virtue of which it is greater than some collections and less than others, provided the collection is discrete, that is, provided the constituent units of the collection are or may be distinct. But when the units lose their individual identity because the collection exceeds every positive existence of the universe, the word multitude ceases to be applicable. I will take the word multiplicity to mean the greatness of any collection discrete or continuous.
Multitude (in mathematics) [Lat. multitudo]: Ger. Mächtigkeit, Cardinalzahl; Fr. puissance; Ital. moltitudine. That relative character of a collection which makes it greater than some collections and less than others. A collection, say that of the A’s, is greater than another, say that of the B’s, if, and only if, it is impossible that there should be any relation r, such that every A stands in the relation r to a B to which no other A is in the relation r.
I shall always use the word multitude to mean the degree of maniness of a collection.
By multitude I mean that quality of a collection by virtue of which it is greater than all those collections than which it is greater.
Multitude is that character of a collection by virtue of which it is more than another collection and less than a third.