Notation convention for $\{1,\ldots,n\}$

I don't know how popular this is but I've seen the convention: $$[n]\equiv\{1,2,3,4,\ldots n\} $$

See for example: http://www.math.cmu.edu/~lohp/docs/math/mop2013/combin-sets-soln.pdf

It depends on the context, but a couple of equivalent formulations I've seen:

• You could say $\{k\}_{k=1}^n$. I saw this often when considering sets of data points, like below, but I see no reason the notation couldn't extrapolate to any set.

$$\{(x_1,y_1) \; , \; (x_2,y_2) \; , \; ... \; , \; (x_n,y_n)\} = \{(x_i,y_i)\}_{i=1}^n$$

• In combinatorics, apparently $[n]$ can be used to represent $\{1,...,n\}$ as touched on in the comments and by Archimedesprinciple.

In homotopy theory, both $[n]$ and $\mathbf{n}$ are common and, to a lesser extent, $\underline{n}$. None of this matters too much, as long as you define your choice of notation clearly in your writing.