# Is there a word or two that can replace 'greater than or equal to'?

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

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

• "Not less than", at least"; "not greater than", "at most". :) Oct 19, 2015 at 22:46
• 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". Oct 19, 2015 at 22:57
• "includes" for sets is abstractly the same relation as "greater than or equal to" for numbers. Oct 19, 2015 at 23:02
• Two or more. Two or less. Oct 19, 2015 at 23:05

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.
• 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, 2015 at 2:39
• @Farid The OP did not restrict answers to a context of formal logic. Let's not presume one. Oct 20, 2015 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, 2015 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. Oct 11, 2016 at 10:45

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.