Symbols:N/Initial Segment of Natural Numbers
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Initial Segment of Natural Numbers
- $\N_n$, $\N^*_n$
The set $\N_n$ is the set of all natural numbers which are less than $n$:
- $\N_n = \set {x \in \N: x < n} = \set {0, 1, 2, \ldots, n - 1}$
The $\LaTeX$ code for \(\N_n\) is \N_n
or \mathbb N_n
or \Bbb N_n
.
Similarly, the set $\N^*_n$ is the set of all non-zero natural numbers which are less or equal to $n$:
- $\N^*_n = \set {x \in \N^*: x \le n} = \set {1, 2, \ldots, n}$
The $\LaTeX$ code for \(\N^*_n\) is \N^*_n
or \mathbb N^*_n
or \Bbb N^*_n
.
Variants
Older literature tends to use $\N$ to mean $\set {1, 2, 3, \ldots}$.
Consequently, the set $\set {0, 1, 2, 3, \ldots}$ needs another symbol to denote it.
The usual technique is to use $\tilde \N$.
The $\LaTeX$ code for \(\tilde \N\) is \tilde \N
.