For example, if a there is a validation message that specifies that a number "must be a value between 1 and 100" does that imply that 1 and 100 are part of the allowed set of values?
I would suggest that 1 and 100 are not part of the allowed range as it states the value must be between 1 and 100. Therefore meaning more than 1 and less than 100.
Am I right?
I agree with your line of thinking because between should be 1 < x < 100.
However that isn't the common usage. I build a lot of web apps and we have focus groups we use and I have ran across this example many many times. When presented with a range it is common practice that if you use the word between that the high and low value of the range is included.
The wording would have to be changed to not include 1 and 100. Maybe, "Specify a (whole) number greater than 1 and less than 100."
So you have to think for the common person filling something out, not the true mathematical thinking (although I agree with you and have lost this battle a few times).
If you don't want to go with the math notation (for which I, too, learned square brackets), the magic word you want is exclusive.
Pick a number between 1 and 100, exclusive.
excludes the endpoints.
Use math notation:
(0, 100) - does not include 0 and 100 <0, 100> - include 0 and 100 (0, 100> - do not include 0, but 100
etc...
