This seems useful but I can't find anything like it.
For example, I might want to say that $\mathbb{N}_{7} = \{ 0, 1, 2, 3, 4, 5, 6 \}$ or $\mathbb{N}_{7} = \{ 0, 1, 2, 3, 4, 5, 6, 7 \}$. Is some sort of notation like that accepted?
Is there a symbol for the first n natural numbers or the natural numbers up to n?
2
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notation
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2I've seen $[[m,n]]$ used for $\{m,m+1,\ldots,n\}$. – 2017-01-27
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3I have seen $[n]=\{1,\ldots,n\}$ – 2017-01-27
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0I don't like it myself, but many authors treat the von Neumann way of representing numerals in set theory as a definition and identify $n$ with $\{0, 1, \ldots, n - 1\}$. – 2017-01-27
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1I've seen $ I_n$ used to denote the set $\{0, 1, \ldots, n\} $ and also $ I_n $ is called a *section* of the natural numbers. – 2017-01-27
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0@RobArthan. Set-theorists like the ordinal version as it is often convenient within that subject . But most people would be puzzled by "If $x\in 9$ then...." – 2017-01-27