Q&A

# Isn't "any, some, or all" redundant? Why not write just "any"?

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Please see the title of this post. In the following quotations, what changes — if anything — if you replace "any, some[,] or all" with just "any"? Don't these authors need just "any"?

I deliberately picked books written by mathematicians, because math requires logic and precision.

### Errors in testing a hypothesis

As already mentioned, a hypothesis is an assumption that may prove to be either correct or incorrect. It is possible to arrive at an incorrect conclusion about a hypothesis for a variety of reasons. Incorrect conclusions about the validity of a hypothesis may be drawn if: • the study design selected is faulty; • the sampling procedure adopted is faulty; • the method of data collection is inaccurate; • the analysis is wrong; • the statistical procedures applied are inappropriate; or the conclusions drawn are incorrect.

Any, some or all of these aspects of the research process could be responsible for the inadvertent introduction of error in your study, making conclusions misleading. Hence, in the testing of a hypothesis there is always

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Language is ambiguous. Mathematics should not be. We can either state our own definitions at the outset, or we can use wording that (hopefully) rules out any of the ambiguous cases.

“Any” may mean “at least one” ($n\ge 1$) or “exactly one” ($n=1$). “Some” generally implies both “more than one” and “less than all” ($1<n<n_\text{max}$), but it is not explicit and there may be exceptions. “All”, of course, means “all” ($n=n_\text{max}$).

“Any, some, or all” is therefore a way to unambiguously indicate $1\le n \le n_\text{max}$ in words.

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