I'm taking a break from proofreading a paper. I'm reading it out loud, because I find this is the best way to catch mistakes; it forces me to look at every word.
There are inequalities in this paper, so the signs ≤ and ≥ come up a lot. How do you pronounce these? When I was in college I pronounced them "less than or equal to" and "greater than or equal to". But sometime around the first year of graduate school I seem to have shifted to "at most" and "at least", which have the obvious advantage of being shorter.
Edit (11:15 pm): It appears I've mentioned this before.
ell-eek and gee-eek.
ReplyDelete"less than or equal to" emphasizes the possibility of equality, and distinguishes ≤ from <. Sure, "At most" means the same thing, but I wouldn't put it past a listener to use "at most" to mean <.
ReplyDelete"less than or equal to" and "greater than or equal to".
ReplyDeleteI don't think the phrases "at most" or "at least" ever escaped my lips when reading a mathematical formula.
Maybe this means I'm an android. But I do use contractions. If I am an android, don't tell me. I don't want to know!
Tangentially related: my C code got a lot clearer when I created AtMost() as a synonym for min() and at AtLeast() as a synonym for max(). I probably use them three times as much as the originals now.
ReplyDeleteIf the distinction does not matter, lesser/greater than. If the distinction matters, add or equal to that.
ReplyDeleteAnd occasionally "not above", "no(t) greater", "no more than" or some similar phrase.
In Spanish we call it:
ReplyDeleteMenor o igual que
y
Mayor o igual que
I always used to say "greater than or equal to" and "less than or equal to" since that was how I was taught whenever it was that I was first introduced to those symbols, but recently I have found myself saying "at most" and "at least" at least some of the time. Funny thing is I am not really sure where I first even heard someone read them that way.
ReplyDeleteBack in the old days before spell checkers, I found it useful to read the text backwards. That way I was not distracted by the actual meaning of the text, so I caught more spelling mistakes. Now we do have spell checkers, but perhaps the same technique could be used to focus enough on the formulas to catch silly mistakes like mismatched parentheses.
ReplyDeleteI personally still use "less than or equal to" and "greater than or equal to". They have a more direct parallel to the cases where equality is excluded than do "at most" and "at least"
ReplyDeleteIn my everyday journal I use these signs to refer to time: "no later than" and "on or after". ( I hope I've got that the right way round). Without the equal part, it's just "before" and "after".
ReplyDeleteI used to say "less than or equal to" and "greater than or equal to."
ReplyDeleteBut I came across this posting on your blog, and ever since it's been "at most" and "at least." Way better.
In German I say »größer gleich« and »kleiner gleich«. Translated word by word this would be »greater equal« and »less equal«.
ReplyDeleteThis reminded me of another matter of style from the December 3 post about Ken Jennings. Someone in the comments mentioned the "septomino" with a hole in it. What do you use? "Septomino" or "Heptomino".
ReplyDeleteSean,
ReplyDeleteI'm going to refuse to answer the question and say I'd refer to a "7-omino". This may or may not actually be what I'd use if I were referring to one of these objects in normal speech.
"ell ee" and "gee ee." Ahh, LaTeX... :)
ReplyDelete