What is correct/better?

  1. We consider questions related to analysis of real numbers and to probability theory.

  2. We consider questions related to analysis of real numbers and probability theory.

An additional question: I do not need "the" before the word "analysis" in those examples, do I?

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    If I were you, I would have used "the". But I don't think not using it causes problems. And both of your statements are true. Choose whichever you like. One more thing: You consider questions to be what? One last last point: If you're gonna use the sentence somewhere public like here, being most understandable is very important, and that means you should avoid repetition as much as you can, as long as it's not considered offensively sarcastic or doesn't demonstrate you as so. – M.A.R. ಠ_ಠ Feb 12 '15 at 11:14
  • @MARamezani Thank you for the comment. I have not understood one point. What do you mean by "You consider questions to be what?" – Sinusx Feb 12 '15 at 11:49
  • If by "consider" you mean the meaning: "Believe to be...". Then that would make the sentence incomplete. I believed you meant that meaning as it's the most common. – M.A.R. ಠ_ಠ Feb 12 '15 at 11:53
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    @MARamezani I think OP is using consider in the sense *take under consideration, examine". – StoneyB Feb 12 '15 at 12:51

It depends on your audience.

If you are talking to mathematicians, you don't need the second “to”, because your audience knows that “analysis of real numbers” and “probability theory” are separate things, and they hear those as separate chunks. So, mathematicians hear the sentence as following this pattern:

Let's go to dinner and a movie.

Let's go to the Museum of Natural History and a movie.

Since you know math, I'll use parentheses to show the grouping in the listener's mind:

Let’s go to (the Museum of (Natural History)) and (a movie).)

However, if your listener had never heard of the Museum of Natural History (and couldn't see the capitalization), your listener could hear it this way:

Let’s go to (the Museum of (Natural History and a Movie)).

In general, how objects get divided among prepositions depends on how familiar phrases, prior knowledge, and common sense influence how a listener “chunks” the sentence.

In your example, you can avoid even the small potential for ambiguity by using the common phrase “real analysis” so you don't need to say “of”:

We consider questions related to real analysis and probability theory.

Conceivably, a naïve listener could hear that as:

We consider questions related to (real (analysis and probability theory)).

but the phrase “real analysis” is so familiar, anyone in the field will hear it as:

We consider questions related to ((real analysis) and (probability theory)).

You don't need “the” before “analysis”, “real analysis”, or “probability theory”. Most names of fields of study do not get an article. For example, one studies “biology”, not “the biology”. One exception is “the calculus”, but while some textbooks have that as their title, I've never heard anyone say it in conversation. There are other exceptions, but that's probably best addressed in a separate question.

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    I think that the parallel structure between "real analysis" and "probability theory" makes the sentence clearer. Humans do love patterns and symmetry; so much so that they will see patterns where there are none if they are in unfamiliar territory. Best to give folks what they would like to see if you can :) – ColleenV Feb 12 '15 at 14:02
  • I upvoted, because I think it's a valid position; but I suggest that a) It may not be the case that readers will know that "analysis of probability theory" is not meaningful - if this is an introduction to a textbook, for instance. (I didn't know it!) b) In any case, written English should follow the rule that "anything which can be misunderstood will be", and be careful to forestall any syntactic ambiguity. – StoneyB Feb 13 '15 at 12:14
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    @StoneyB Indeed the idea is that whether there is ambiguity depends on your audience. I'll edit to make that clearer. And actually, the premise is not that "analysis of probability theory" isn't meaningful, it's that in the minds of mathematicians, "probability theory" is a tightly fused little chunk and "analysis" has a special meaning mainly associated with real numbers, so they're unlikely to associate "analysis of" with "probability theory" unless you give them no other alternative. – Ben Kovitz Feb 13 '15 at 12:39

Yes, in this instance you do need the second to -- it changes the meaning

With the second to, probability theory is clearly marked as conjoined with analysis of real numbers as the object of related to; the sentence means

We consider questions related  to analysis of real numbers
[we consider questions related] to probability theory

Without the second to, probability theory is taken to be conjoined with real numbers as the object of of; the sentence means

We consider questions related to analysis  of real numbers
[we consider questions related to analysis] of probability theory.

  • For your above comment I guess this is just another example that made J.R. shout: Details, please! :) Furthermore, The author gives no clue that he meant the former concept you mentioned or the latter. – M.A.R. ಠ_ಠ Feb 12 '15 at 12:56
  • @MARamezani Well, OP does give one fairly important clue: the sentences make sense under one reading and not under the other! :) – StoneyB Feb 12 '15 at 12:59
  • I didn't realize this was a riddle! :) – M.A.R. ಠ_ಠ Feb 12 '15 at 13:03

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