## 2.5 Notation

The natural integers are elements of $\mathbf{N} = \{ 1, 2, 3, \ldots \}$. The integers are elements of $\mathbf{Z} = \{ \ldots , -2, -1, 0, 1, 2, \ldots \}$. The field of rational numbers is denoted $\mathbf{Q}$. The field of real numbers is denoted $\mathbf{R}$. The field of complex numbers is denoted $\mathbf{C}$.

Comment #3544 by Laurent Moret-Bailly on

Do you really mean that $0\notin\mathbf{N}$?

Comment #3676 by on

Yes, I do. Also, I think it would be too late to change it now. Sorry if this isn't the standard convention.

Comment #6297 by RJ Acuña on

Of course it doesn't matter because $\left(\mathbf{N} \cup \{\0}\right)\cong \mathbf{N}$. It's quite standard in number theory to say $0\not\in \mathbf{N}$. Some people find $0\in \N$ desirable because it makes $\mathbf{N}$ into a monoid. It's a matter of taste.

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