I am confused on why these naming conventions are the way they are. The symbols > and < are usually written as "greater than" and "less than".

The opposite of "less" is "more", isn't it? Though those words describe quantities only, which might not be desired if you're talking about a measure of size instead.

So, sticking with "greater than", shouldn't the opposite be called "smaller than"?

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    The names come from a time when the more common antonym of "greater" was "lesser", as in "a great man" vs "the lesser of two evils", or the general trend in early taxonomic systems to give informal names like greater vs lesser sand plover. We don't use greater or lesser in this sense much nowadays (do you ever say "his slice of cake is greater than mine"?), but the names have stuck for the mathematical symbols, as they do. – Dan Bron May 31 '17 at 9:35
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    To be pedantic, the opposite of "greater than" is "less than or equal to"... – user888379 May 31 '17 at 16:16
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    Those symbols are MATHEMATICAL symbols. They mean whatever meaning mathematics assigns to them. And in mathematics the opposite of "greater than" is "less than or equal to". – Hot Licks Aug 30 '17 at 12:17
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    Please reconsider, @Hot Licks. OP is not asking what is the mathematical antonym of 'greater than', but "shouldn't the opposite be called "smaller than"" -- it's not only in mathematics that the commonly used antonym of 'greater than' is 'less than' and not 'lesser than': there is the common expression 'the whole is greater than the sum of its parts', as applied to effectively co-ordinated group activities, and the antonym would be 'less than' as in 'disunity makes them less than the sum of their parts' -- so it's an English question in asking why is the antonym used inconsistently here? – English Student Aug 30 '17 at 12:35
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    @HotLicks the question is on-topic. it is about how the various English words are used or not to describe the very ordinary mathematical concepts. – Mitch Aug 30 '17 at 12:40

One possible reason that mathematics might have come to use greater than and less than as opposed to (say) larger than and smaller than might be that they were more natural translations from Latin.

Mathematics was largely done in Latin until the 17th century. The Latin terms were majorem quam and minorem quam, as can be seen by the first definition of the > and < signs in Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas by Thomas Harriot (see Wikipedia):

"Signum majoritatis ut a > b significet a majorem quam b" and "Signum minoritatis ut a < b significet a minorem quam b."

Major is the comparative form of magnus, which I assume was generally translated as great, since its range of meanings is much broader than large. (E.g., Charlemagne was called Carolus Magnus, or Charles the Great. Charles the Large wouldn't have meant the same thing at all.) Thus, major would naturally be translated as greater.

Minor is the comparative form of parvus, which again has a much broader meaning than small (small, cheap, ignorable, unimportant). The natural opposite of greater in English that is compatible with this broader meaning would be less or lesser.

  • Good answer. But it motivates a follow-up: Why not "lesser than" instead of "less than"? – A. Donda Jul 21 '20 at 6:42

As you might suspect, the symbols (and thus their names) come to us from the world of mathematics. According to Wikipedia:

The symbols < and > first appear in Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas (‘The Analytical Arts Applied to Solving Algebraic Equations’)...

So, in the world of math, as I understand it, less is not the same as smaller.

But then, why greater instead of more? According to this page:

The 3 Rules for MORE/GREATER/LESS/FEWER than…

  1. If COUNTABLE (dogs, apartments, opportunities, agencies, people)
    -> then Use MORE/FEWER than combination

  2. If COUNTABLE, but related to time, distance, or money OR if NOT-COUNTABLE
    -> then Use MORE/LESS than combination

  3. For BOTH COUNTABLE & NOT-COUNTABLE, if there is a comparison made between the LEVEL or DEGREE or NUMBER of something
    -> then Use GREATER THAN/LESS THAN combination

So, because there is a comparison going on, we use greater than/less than. (Note that that site includes no references, but if you want something more definitive, I'm sure that the Google can help out.)

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    I think the question is why rule #3. It sounds like a "rule" that just reflects usage. In that case, this answer is "just because". – Drew May 31 '17 at 17:30
  • To answer that question, you're going to have to find someone smarter and more knowledgeable than I. – Roger Sinasohn May 31 '17 at 19:27
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    And I............ – Drew May 31 '17 at 20:11

Surely this confusion comes from using the same mathematical symbols to compare differing data types. Not only are they applied to both countable and noncountable entities, in computer programming, they are applied to dates. In which case, we should be using 'earlier than' and 'later than'. In theory, this could also include other comparisons, such as 'higher than' and 'lower than'. Why 'greater than' and 'less than' have passed into common usage, is probably due to the vast majority of people abandoning the grammatical difference between a number and a quantity and 'great than' just sounds weird, whereas 'less than' doesn't, for some strange reason, which I can only attribute to good old common usage.

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