1.4 Stanley's Brace Notation & Ellipses

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 1.1 Set

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Stanley's Brace Notation & Ellipses

Let's define the set of the first ten positive integers. We will call this set

[10] = {1, 2, 3, \dots, 10} = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

$\dots$ means "and so on" leaving the work to the reader

The first description of the set suggests to the reader that we want to list all the integers from 1 to 10. The second description explicitly lists out the elements of the set. The benefit of using the ellipsis " $\dots$ " is brevity and ease of reference. However, it is important to watch out for ambiguity when working with ellipsis.