the number of things, beginning with 0, 1, 2, 3, ..., to include infinite cardinal numbers. there are many different cardinal numbers. infinity can be defined in one of two ways: infinity is a number so big that a part of it can be of the same size; infinity is larger than all of the natural numbers. there is a smallest infinite number, "countable infinity". it is the counting number for all of the whole numbers. it is also the counting number of the rational numbers. the mathematical notation is the hebrew letter aleph with a subscript zero; formula_2. it is spoken "aleph naught".