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I was curious about how English articles work with cases such as:

For all of the simulations, the B = 15 mT, the f = 10 kHz.

The B and f are of course defined earlier in the text and are used in the same context in the entirety of the text as well. Is it ok to write "the" before each parameter in such sentences? Or should I omit it?

I couldn't find a source that gives a definitive answer on how to use English articles in equations like or equalities like this. I think it's better to omit articles in this case but when I read the sentence in my mind, I read it like "B equals 15 mT" and feel like there should be an article.

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  • I’m voting to close this question because it's maths-specific rather than standard everyday English. Mathematics.SE. Oct 1, 2021 at 15:22
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    @EdwinAshworth It's not: it's how to treat something like B here in English, which may well be different to how it's treated in other languages. I can imagine that French could easily take an article.
    – Andrew Leach
    Oct 1, 2021 at 15:27
  • @AndrewLeach Yes, precisely as you said, we don't even have articles in my language, and we would write the sentence in an entirely different manner. Oct 1, 2021 at 15:41
  • @AndrewLeach Ask 100 people whether B = 15 mT written on a piece of paper is (a) everyday English or (b) more maths / science orientated. If there are different national conventions in mathematical representation, this still doesn't make this a topic of standard everyday English. Oct 1, 2021 at 16:35
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    But this site isn't restricted to everyday English. Abstruse and unusual usages of English are also welcome. If the question is not language-specific, by all means migrate it to a specialist site; but where it deals with a point of English and the answer may differ for other languages, it is highly likely to be on topic here.
    – Andrew Leach
    Oct 1, 2021 at 16:40

2 Answers 2

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B and f are treated as names for the things they represent. Names don't take articles, unless you are The Donald — and even then, Donald is treated rather like a title.

If you were to write "the magnetic flux density was 15mT and the frequency was 10kHz," then you would need an article with the common nouns. Using symbols, you have given the particular instance of that common noun a name.

Consider a similar situation with sentences like "The man had three coins" and "Andrew had three coins": you have given the particular man a name. It doesn't take an article.

You're actually right to read it as "B equals 15mT" or perhaps "B equals fifteen milliteslas".

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  • Thanks for the answer! Oct 1, 2021 at 15:29
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Just an add-on to A.L.'s answer. When we refer to a variable in an equation or formula, the article is sometimes used and sometimes omitted. This may depend on whether one is referring to the variable as an instance of a symbol or one is referring to its meaning (what the symbol/letter represents) or its (numeric) value. The article is more common when the variable is being referenced as a (written) symbol.

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The F in Equation 13.5 is often replaced by a sum of forces to achieve... ref

... the F in Equation 12.1 is an unobserved, or latent variable. ref

but

As mentioned above, F in Equation 3 is the fraction of ... ref

First we assume that ... so f in equation (22) may be substituted from ... ref

... was used to determine f in equation 12 ref

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  • We encountered a problem when I was teaching in that in physics, letters directly represented lengths, weights etc. We'd end up with L/cm = 16. In maths, L stands for the numerical value of the length measured in the required units. L = 16. Oct 1, 2021 at 18:20

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