"we denote by n an integer" instead of "n denotes ..."?

manthano

Member
Hello,

occasionally, I come across sentences like the following ones: "We denote by n an arbitrary integer" or "By C we will always denote a circle". Are these sentences correct? I have got a certain feeling that they are not (which is supported (corroborated), I think, by what merriam-webster.com says about the word "denote"). Shouldn't it rather be "(The symbol) n denotes an arbitrary integer" or "C will always denote a circle"?

manthano

• Beryl from Northallerton

Senior Member
This is maths, and maths is a subset of logic (if your theology will allow that ), so we are into the realm of jargon - sad, but inevitable.
This is the Logic usage of 'to denote', meaning to indicate the objects comprehended in a class.

So, standard in Maths, but maybe a little 'out there' in English. What ever happened to "Let n be an integer (element of...)"?

DocPenfro

Senior Member
Shorter OED: "denote = express by a symbol". This usage (one of five offered by this dictionary) may not be "correct" in the sense of traditional, but it is acknowledged by a reputable dictionary. As Beryl says, if you want to learn the best English, you are probably not going to find it in the pages of Maths books.

Beryl from Northallerton

Senior Member
As Beryl says, if you want to learn the best English, you are probably not going to find it in the pages of Maths books.
Well now, I didn't go so far as to say that!

manthano

Member
What ever happened to "Let n be an integer (element of...)"?
It is (still) *the* standard construction to introduce and define symbols in maths. And you are completely right, I can hardly think of any context where "We denote by n an arbitrary integer" should be preferable to "Let n be an arbitrary integer" -- I should have chosen a different sample sentence like "If not explicitly stated otherwise, we will denote by c the speed of light in what follows". In sentences with such *global* conventions mathematicians wouldn't use their beloved "let" construction, I think. (At least, I wouldn't )