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Are there rules about using “that” to join two clauses?

In mathematical parlance it is customary to write, for example, "One wishes to prove that the following is true." Is the word "that" in the preceding sentence superfluous or necessary and correct?

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The word that in your example is not necessary for clarity. In fact, you could shorten the statement to:

One wishes to prove the following:

The omitted that and ending is true will be assumed by the reader.

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    Or even, "One wishes to prove:" followed by the thing to be proved.
    – Charles
    Commented Oct 18, 2011 at 17:05
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    @Charles If this was a test question or textbook problem, it could be further shortened to just "Prove:"!
    – jimreed
    Commented Oct 18, 2011 at 17:20

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