[Math] Intervals: examples of open intervals; fencepost errors

Open intervals in programming are rare.

For example, if it's impossible to divide by 0 and infinity, the valid intervals for divisor are: (-inf, 0) and (0, +inf). Hence we include however small numbers but not zero. And however large numbers, but not infinity.

The major source of fencepost errors is a confusion between closed and half-open intervals.

If you're aware what intervals do you use in each loop, you'll reduce number of errors significantly.

Also, note that Edsger W. Dijkstra was a famous proponent of half-open intervals and arrays starting at zero index.

In his famous paper, he enumerates half-open, half-closed, closed and open intervals and offers to choose best suited for programming:

a) 		2 ≤ i < 13
b) 		1 < i ≤ 12
c) 		2 ≤ i ≤ 12
d) 		1 < i < 13

(the post first published at 20251219.)

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