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In a mathematical context, which of the following options is more appropriate?

  1. Since the fact A is true, we have B=C.
  2. Since the fact A is true, we have that B=C.
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closed as off topic by Bill Franke, cornbread ninja 麵包忍者, Robusto, tchrist, StoneyB Jan 4 '13 at 23:59

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I'd sooner write 2., but what is A, here? –  Branimir Ćaćić Jan 4 '13 at 14:39
    
I'd write neither because neither reads like English to me. Instead: "Because A is true, B = C." –  user21497 Jan 4 '13 at 14:42
    
@Bill: If OP isn't a native speaker (and maybe even if he is) I think he'd pick up extra brownie points for coming out with such a context-specific (but valid) usage - Go for it, zacarias! :) –  FumbleFingers Jan 4 '13 at 15:44
    
@F: If he wants real English instead of maths jargon, I'll give him the brownie points. If he wants maths jargon, he should ask a mathematician. I had to learn that abolish, a legal term, is also a piece of microbiological jargon that means to totally inhibit. This isn't English usage but biomed jargon usage. –  user21497 Jan 4 '13 at 15:47

1 Answer 1

Both of these constructions are commonly used in mathematics. In ordinary (not mathematical) present-day English, these would be written as

... we have the fact that B = C.

Consider:

We have the fact that John is an idiot.
*We have that John is an idiot.
*We have John is an idiot.

Neither of the latter two constructions would be admissible in ordinary English, and I can find no evidence in Google books that they ever were admissible (although the middle one sounds marginally better to me, which means that if you had to choose one of these two, I would recommend that one). So I'd suggest rewriting it as one of the following:

Since A is true, we have the fact that B = C.
Since A is true, we learn that B = C.
Since A is true, we know (that) B = C.

(Or any of the other many ways of expressing this that are also grammatical in ordinary English.)

Note that I have dropped "the fact" from the first part of the sentence. Again, this is because it would not be grammatical in ordinary English:

*Since the fact the project was bungled, we know that John is an idiot.
Since the project was bungled, we know that John is an idiot.

Unlike the second part of the OP's original sentence, I don't believe it is even acceptable in mathematical English.

EDIT: I just realized that maybe you meant "since the fact A is true" to be parsed as "since (the fact A) is true" rather than "since the fact (A is true)". If that is the case, you can ignore the second part of my answer.

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Since OP is specifically asking about usage in a mathematical context, I see no reason to suggest rephrasing. As you say, since [some truth] we have [that] [some other truth] is perfectly normal in such contexts. But I do think it sounds a bit more "formal/academic/authoritative" than the even more common we see that... –  FumbleFingers Jan 4 '13 at 15:41
    
@FumbleFingers: it seems to me that since in this case, it's easy to change this sentence to comply with standard English grammar, you might as well do it (although I am sure that there are many cases where I didn't in my papers). –  Peter Shor Jan 6 '13 at 14:09

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