Category:Definitions/Numbers

This category contains definitions related to Numbers.
Related results can be found in Category:Numbers.

There are five main classes of number:

$(1): \quad$ The natural numbers: $\N = \set {0, 1, 2, 3, \ldots}$

$(1 \text a): \quad$ The non-zero natural numbers: $\N_{>0} = \set {1, 2, 3, \ldots}$

$(2): \quad$ The integers: $\Z = \set {\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots}$

$(3): \quad$ The rational numbers: $\Q = \set {p / q: p, q \in \Z, q \ne 0}$

$(4): \quad$ The real numbers: $\R = \set {x: x = \sequence {s_n} }$ where $\sequence {s_n}$ is a Cauchy sequence in $\Q$

$(5): \quad$ The complex numbers: $\C = \set {a i b: a, b \in \R, i^2 = -1}$