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I've seen, "second largest" being used more often. Is there any special reason that, "second maximum", is not a correct thing expression?

For example, if I have an array of numbers: 1,2,3, is it correct to state that 2 is the second maximum number?

0user
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    'Maximum' tends to be used for counts of articles, people etc (and of course measures like heights, weights, temperatures) rather than pure numbers. Also, in pure maths, a maximum is a point on a curve. 'Second maximum' sounds outlandish when used of numbers. It's more a style thing than a logic thing. We have to live with it. – Edwin Ashworth Oct 10 '19 at 18:58
  • @0user would you say "the second unique value" ? – Weather Vane Oct 10 '19 at 19:19
  • @0user Second greatest, second largest, second biggest, but not second maximum. See the answer below. – Davo Oct 10 '19 at 20:51
  • Second maximum would make complete sense in the game of snooker. In that game, a maximum is the highest possible score of 147 points. Therefore, a second maximum would be the second time a player has achieved that score. The same could be said for math, where something has reached a maximum value for the second time. Of course, that doesn't sound like the exact context of your question. Then again, the word maximum itself doesn't make much sense with respect to your question either. – Jason Bassford Oct 14 '19 at 01:34

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In my experience "maximum" refers to a singular value. In calculus you can have "local maximum" of a curve that is not the global maximum of the curve.

In statistics, however, you can rank values. You can have a "highest rank" and "second highest rank". But even there I don't hear "second maximum" as a common phrase.

There is also "sub-maximum" but I hear it in things that aren't easily counted. "He gave a sub-maximal effort".

Josh English
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