Anyone working as a computer programmer has at some point had to precisely distinguish between intervals and interval boundaries.

Intervals are delimited by interval boundaries. For instance, 1-2 denotes a single interval. In this case the interval is delimited by 2 interval boundaries (1 and 2).

There are always 1 more interval boundaries than there are intervals (since intervals are closed).

A similar relationship can be seen in languages that index arrays/collections from 0. The total number of elements (or count) in an array is 1 greater than the number of indices.

Having recently worked on drawing lines on 2D surfaces with DirectX I’m beginning to think of pixels as intervals and vertices as interval boundaries.

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