[Math] symbol for the set of integers from 1 to N

elementary-set-theory

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About Math notation: the set of the first $n$ natural numbers

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Is there a special symbol for the set: $$
\{1, 2, 3, \dots, n\}$$,
or $$\{x| 1\leq x\leq n, n \in \mathbb{Z} \} $$?

Best Answer

These are the usual notations (the second is borrowed from computer science):

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Elementary Set Theory – Symbol for the Set of Whole Numbers

To summarize what has been said in the comments, there are no "official" symbols. Use whichever notation you feel most comfortable with, as long as it makes sense and can be easily understood by the general audience.

Some examples include:

$\mathbb{Z}_{\ge 0},\mathbb{Z}^{+}\cup\{0\},\mathbb{N}\cup\{0\},\mathbb{N}_0$

Also note that because of different conventions, what you refer to as "whole numbers" may or may not include zero. From Wikipedia:

There is no universal agreement about whether to include zero in the set of natural numbers: some define the natural numbers to be the positive integers {1, 2, 3, ...}, while for others the term designates the non-negative integers {0, 1, 2, 3, ...}.

Elementary Set Theory – Symbol for Set of Odd Natural Numbers

I don't recall seeing too many places that gave a specific notation to the set of even or odd numbers. Your notation of $2\mathbb N+1$ seems quite reasonable.

As with all notational problems, my usual tip is to find something that seems reasonable and simply declare it in the first few lines (or when you need to use it):

Let $\mathbb O$ denote the set of positive odd integers.

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Related Solutions

Elementary Set Theory – Symbol for the Set of Whole Numbers

Elementary Set Theory – Symbol for Set of Odd Natural Numbers

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