Are there more proper terms for "between, inclusive" and "between, exclusive"?

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I searched for this, but all I found was an English usage result. However, I am strictly asking about ranges of numbers, not "normal" English.

So, are there a terse terms for:

• inclusive between, as in 1 is between 1 and 5
• exclusive between, as in 3 is between 1 and 5, but 1 is not

Maybe something sporty like exobetween and endobetween?

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1 Answer

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Although not as sporty as "endobetween" and "exobetween", mathematicians generally use the adjectives "closed" and "open" to describe the inclusion or exclusion of endpoints in an interval (range) of real numbers.

Thus $(0,1)$ is an open interval, excluding (not containing) the endpoints, and $[0,1]$ would be the corresponding closed interval resulting from including both endpoints.

Another paradigm from mathematical terminology would be that used of inequalities, namely strict (excluding the boundary/equality) or weak (including the boundary/equality). Thus IsBetweenStrict should be expected to reject the endpoints, while IsBetweenWeak should be expected to accept the endpoints.

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