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I found several teachers using the first structure, i.e. "with X equals 3", while some others using the second one, and all of them are native English speakers. Here're some examples of the first structure:

  • We'd start with X equals 3. (source)
  • You've got an atom in the general position 96l with x equals something. (source)

My understanding is that the second one is more popular than the first one because "with + object" is often followed by an adjective in form of a gerund verb or past participle.

I've run through the available examples on Longman and Oxford dictionaries and found no instances of the first structure. So for the second structure I think one possible explanation is that "X equals 3", as the whole, acting like a noun phrase. Is that explanation valid or are there any other explanations for it?

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    "With X equals 3" sounds wrong to me. As you say, "with" takes either a noun phrase or a noun phrase plus a complement. Maybe they're confusing it with "When X equals 3" or something else? Mathematicians aren't always known for their grammar.
    – Stuart F
    Nov 20, 2023 at 10:39
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    I would say with T equal to 35, incidence of heatstroke is H Nov 20, 2023 at 10:55
  • @StuartF, for your reference: here's the one of the videos, youtu.be/Ra9feLehKwA?si=lw-N_KUkfKxe-xdI&t=46
    – Tran Khanh
    Nov 20, 2023 at 15:02
  • And here's another one, youtu.be/dGd519SL114?si=EW8o_aHRdQ4KsMLF&t=2082
    – Tran Khanh
    Nov 20, 2023 at 15:05
  • Can you edit the relevant sentences from the videos into your post? The context of the rest of the sentence is likely to affect whether it's grammatical or not.
    – Laurel
    Nov 20, 2023 at 17:56

1 Answer 1

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To my ear, [with] X equals 3 sounds more like the result of evaluating an equation, rather than setting a variable as a "parameter". That implication is less noticeable in [with] X equal to 3, but I think they're both "sub-standard" compared to...

with X set to 3

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  • Or maybe where X equals 3. This kind of construction is used for instance to complete a definition, as in “Energy and mass are related by the equation E = mc <sup>2</sup>, where c is the velocity of light in a vacuum.” Nov 20, 2023 at 15:16
  • Yes, but usually if we have where [symbol] equals / = [value] after an actual equation, the "[value]" part is a verbal description, rather than a number. "the velocity of light in a vacuum" in your example, not "186,000" (miles per second). And that can't be "set to" some different value, since it's a constant. Nov 20, 2023 at 15:23
  • And in such definition-completion contexts, the fragment following where must be a syntactically complete (sub-) sentence. Nov 20, 2023 at 15:24
  • I agree about verbal rather than numerical. Nov 20, 2023 at 15:25
  • @FumbleFingers, "set" in that case is still in the form of an adjective right?
    – Tran Khanh
    Nov 21, 2023 at 7:19

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