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Background:

I am finding minimum distances from a certain process, and then I do the same for another data set. Then from all those selected minimum values, I want to get the minimum value.

In that case, if I say smallest minimum, then would it be in formal English? Because I am confused how I can say minimum of minimum.

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In that context, I think smallest minimum sounds just fine, although you'd want to be careful if:

  • you're writing to a specialized audience, and the scientific literature calls for a different word to be used in that domain, or
  • another word might work better than smallest. For example, if we were analyzing a set of temperature readings, I'd probably recommend lowest minimum instead of smallest minimum.
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"smallest minimum value from A set of minimum values."

This means to me that you have constructed a set of values from the minimum values of several other sets and now you are referring to the smallest minimum value of a set of minimum values. If it is so your sentence is correct (it just missing the article "a").

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