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Can we say following sentence:

Let (T, F) be a locally constant function which defined on Example 1, where T:X---->R.

or we have to say

Let (T,F) be a locally constant function where T:X---->R, which defined on Example 1.

Also, which is correct, "on Example" or "in Example"?

  • ...which is defined by / in / with Example 1. Several prepositions are "acceptable" here, but on isn't one of them. – FumbleFingers Sep 11 at 12:30
  • Agreed with FumbleFingers. "Where" also isn't appropriate unless you change the structure to something like "where it was defined in Example 1". – JRodge01 Sep 11 at 12:35
  • @FumbleFingers Thanks. what about sentences?which one is correct? – R R Sep 11 at 12:38
  • @JRodge01 :Thanks. what about sentences?which one is correct? – R R Sep 11 at 12:39
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    Couldn't you have come up with an example that doesn't feature inscrutable algebraic expressions? This site is concerned with English, not mathematical notation. – FumbleFingers Sep 11 at 12:54
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Both mean the same, but grammatically both are wrong. The correct will be:

Let T be a locally constant function which is defined in Example 1, where T:X---->R.

OR

Let T be a locally constant function where T:X---->R, which is defined in Example 1.

I'd personally prefer "as defined in Example 1." instead of using "which".

Also, "in, by or with" can be used, but never on

  • I disagree that both mean the same. Even though I don't understand the sentence, I know enough to say that which either refers to "a locally constant function" OR to "T:X---->R", depending on where it's placed. And since we're told that the locally constant function is T, I don't see how that can be exactly the same thing as T:X---->R. I suppose it's at least possible that in your second version, which refers back to just R - but again, R can't be the same as T. – FumbleFingers Sep 11 at 12:49
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    You'll have to enlighten me. I have an A-Level in maths and a degree in English, but I don't know what T:X---->R means, and I've no idea what syntactic category to assign to that "text". – FumbleFingers Sep 11 at 13:05
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    @FumbleFingers If you don't know what it means, you can't claim they don't mean the same thing. Syntactically, forget about the meaning. (1) which X, where Y and (2) where Y, which X. This is roughly the equivalent of (1) if X, then Y and (2) Y, if X. Inasmuch as the meaning is unknown, I think it's likely that the syntax makes the two constructions equivalent. Therefore, I essentially agree with this answer. So, +1 from me. – Jason Bassford Sep 12 at 4:21
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    @FumbleFingers Your example makes use of different specific syntactical constructions. You change the noun to which which applies. It's not the same type of thing. – Jason Bassford Sep 12 at 12:29
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    @FumbleFingers What you did was move which without also moving the noun it was attached to. That's not what the example in the question is doing. Both which and where are being moved along with their attached nouns. You break the two up; the example in the question does not. – Jason Bassford Sep 12 at 14:15
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Neither of your examples are correct, and I don't believe you're mathematically formatting your functions correctly either.

Let (T, F) be a locally constant function which defined on Example 1, where T:X---->R.

should likely be

Let f(T, F) be a locally constant function where T:X->R.

There were 3 changes:

  1. f() is how you normally denote a function.

  2. Unless it is imperative that you call back to example 1, I wouldn't. Add it as a foot note or as a second sentence if needed, or as "as defined in example 1" if you really want it in-line.

  3. I'm unfamiliar with what you're conveying with T:X---->R, but assuming that T is going to cover a range of values from X to R. Context may be helpful, but for word processing sake, you should shorten it to T:X->R.

Your word processor's math formula editor may be better so you can input the correct visual without having to transcribe it to words and circumvent the problem altogether.

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