The value of function f(x)=ax+b is positive when x is positive where a is non-negative real number and where b is positive integer.

Is there any difference as I omit the second "where" as follow?

The value of function f(x)=ax+b is positive when x is positive where a is non-negative real number and b is positive integer.

The comments in both following posts said it's syntactically fine.

  1. A relative clause with multiple prepositions
  2. Which did X and which was Y

The second post said it's unaesthetic. So, is it improper to omit the relative pronouns after the conjunction "and" in formal article? But why does the relative pronoun in textbooks seems like constantly been omitted? Or it's just some writing style?

For example: enter image description here


enter image description here

Thanks in advance!!!

  • 2
    It's fine (actually quite normal) to omit it, but the person might have said it's unaesthetic because you are using two different subordinating conjunctions (that's what I'd call "when" and "where" in this sentence) for no apparent reason. (You're also missing a couple of determiners.) May 23, 2022 at 20:48
  • Thank you for point that out and forgive my poor grammars. I’ll try to bring the determiners back. Again thanks!
    – Wade
    May 24, 2022 at 10:12

1 Answer 1


You've got two different descriptions of the notation -- one for the coefficient values a and b, which are not variables of the function, and one for the range of x, which is a variable. They should be separated, and separately placed in the definition, so as not to confuse coefficients with range variables.

  • The value of the function f(x)=ax+b (where a is a non-negative real number
    and b is a positive integer) is positive whenever x is positive.

It's a good idea to have only one where to cover both coefficients, in the parenthesis, and then to use when (or, better, whenever, to indicate variability) for the variable.

  • 1
    Thanks for your clear explanation it helps me a lot! After rearranging the sentence, it indeed look more pleasant than the one I wrote. Thank you!!
    – Wade
    May 24, 2022 at 10:17
  • This is just the English of what mathematicians would use notation for (a !=0, b >0, a,b in I) May 24, 2022 at 14:52
  • Hmm. It seems odd that a ∈ ℝ⁺ ∪ {0} whereas b ∈ ℕ May 24, 2022 at 16:15
  • I haven't got the right symbols on my Windoze machine. May 24, 2022 at 18:29
  • 1
    Please forgive me if I’m being rude. Since I’m not a native speaker, I’m afraid that I may use some word or grammar that is impolite. Thanks!
    – Wade
    May 24, 2022 at 21:43

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