2

... alternately, 'less than or equal to'?

If nothing exists, can you suggest something new to be widely adopted?

  • 2
    "Not less than", at least"; "not greater than", "at most". :) – Dan Bron Oct 19 '15 at 22:46
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    If there were a convenient (yet unambiguous) term, mathematics would use it, I'm sure. But we still struggle along with "greater than or equal to". – Hot Licks Oct 19 '15 at 22:57
  • "includes" for sets is abstractly the same relation as "greater than or equal to" for numbers. – Greg Lee Oct 19 '15 at 23:02
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    Two or more. Two or less. – Ricky Oct 19 '15 at 23:05
4

The term at least is close in meaning to greater than or equal to. Example of usage:

  • The number of oranges in that bag is greater than or equal to twelve.
  • There are at least twelve oranges in that bag.

Similarly, the term at most is close in meaning to less than or equal to. Example of usage:

  • The number of oranges in that bag is less than or equal to twelve.
  • There are at most twelve oranges in that bag.
  • 1
    You're right, but this doesn't go very well with mathematical and logical context. Compare "The square root of 2 is greater than or equal to 2" to "The square root of 2 is at least 2". The second one sounds like an opinion-based estimation. Not duly formal. – Færd Oct 20 '15 at 2:39
  • @Farid The OP did not restrict answers to a context of formal logic. Let's not presume one. – MetaEd Oct 20 '15 at 2:51
  • That's fair, but I'd personally love to find a word that works well in that context, because that word would work for me! – Færd Oct 20 '15 at 3:08
  • @Færd The positive square root of 2 is more than 1 but less than 2, however the positive square root of a half is more than a half but less than 1. I don't find any problem with the terminology in mathematics but I'd be more likely to express it in symbols (<,<=, >=,>) which, when one reads them, become 'less than', 'less than or equal to', 'greater than or equal to' and 'greater than'. However I'm sure that no one would object to 'at most' and 'at least' as interpretations of the symbols as these are exact descriptions of their meanings. – BoldBen Oct 11 '16 at 10:45
0

The trick with these phrases is to find the phrase that means the opposite and then invert it.

If something is greater than or equal to something then the opposite must be less than. So inverted would be not less than.

If it's less than or equal to then the inverted opposite would be not more than or sometimes no more than.

Alternatively you can take the equal to value and imply an acceptable variance direction. For instance at least X would be equal to or greater than X and at most Y would be equal to or less than Y.

Phrases like up to Z can be somewhat ambiguous and could include or exclude Z.

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