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I frequently write technical texts, in particular mathematics. As the subject matter tends to be difficult, I have made it a habit to augment each potentially confusing phrase with a clarification. The abbreviation i.e. has become my trusted tool for this task.

However, I have never been very satisfied with i.e., mostly because I am beginning to use it like a unique grammatical construct, even though it is just an abbreviation. My problem is that I find the commonly cited synonym "that is" to be worse, I think it breaks the flow of sentences too much.

Let me demonstrate this with a typical example

Assume that this is not true, i.e. that there are counterexamples X and Y such that the statements Y < X and X < 2Y are false.

If I want to replace "i.e." by "that is", I have to remove the second "that"

Assume that this is not true, that is there are counterexamples X and Y such that the statements Y < X and X < 2Y are false.

but I find this version to be less readable than the original. The reason is that the i.e. invites the reader to repeat the preceding clause, i.e. the reader can enhance the flow by reading it as follows:

Assume that this is not true, i.e. (assume) that there are counterexamples X and Y such that the statements Y < X and X < 2Y are false.

If I wanted to enhance readability with "that is", I would have to repeat a part of the first clause explicitely in the text

Assume that this is not true, that is assume that there are counterexamples X and Y such that the statements Y < X and X < 2Y are false.

Such explicit repetition would grow old really fast, though.

The underlying problem seems to be that the phrase "that is" carries no meaning by itself, it is again a shorthand for "which means that", "this says that" or "in other words".

My question is:

What are other alternatives to i.e. that can I use in the sentence above?

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I would assert that you probably often could (and should) break up your sentences into shorter sentences: Assume that this is not true. Assume that there are counterexamples X and Y, such that the statements Y < X and X < 2Y are false. –  JLG May 23 '12 at 12:47
    
@JLG: Alas, the reformulation you offer changes the meaning slightly, with the unfortunate effect that your version becomes very confusing. My audience will understand this as "Assume something. Assume something else." and will take a while to figure out that these two assumptions are actually the same. That's why I need the conjunction "i.e.". –  Greg Graviton May 23 '12 at 13:15
    
Maybe: Assume that this is not true; assume that there are counterexamples X and Y, such that the statements Y < X and X < 2Y are false. –  JLG May 23 '12 at 13:29
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3 Answers

What about namely?

Assume that this is not true, namely, that there are counterexamples X and Y such that the statements Y < X and X < 2Y are false.

Assume that this is not true--namely, that there are counterexamples X and Y such that the statements Y < X and X < 2Y are false.

Some recommend you use a dash if a comma comes after "namely," but I think it's redundant since the dash signifies namely.

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I like that. I use namely a lot, but never made the connection with i.e.. It does seem to have a slightly different connotation, though. "I want to eat a tasty bubble gum, namely the pink one." vs "I want to eat a tasty bubble gum, i.e. the pink one." In the first case, there could also be a green gum that is tasty, while the second sentence implies that only the pink gum is tasty. –  Greg Graviton May 23 '12 at 13:24
    
A question concerning punctuation: in your sentence, I would omit the comma after namely. Which punctuation is preferable? –  Greg Graviton May 23 '12 at 13:35
    
In the math example, the commas on both sides of namely are parenthetical commas, so both are necessary (don't omit). In the bubble gum example, you are using namely to clarify a direct object (not a clause), so you don't need the comma. –  jeffclef May 23 '12 at 13:53
    
Yes, use both commas, as that makes it more readable. In fact, in your examples above, an extra comma would help solve your problem: "Assume that this is not true, that is, assume that there are counterexamples X and Y..." (You can see that same construct illustrated here) –  J.R. May 23 '12 at 14:21
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What you could do is use punctuation. I think I prefer a dash, but colon and comma could work.

Assume that this is not true: that there are counterexamples X and Y such that the statements Y < X and X < 2Y are false.

Assume that this is not true, that there are counterexamples X and Y such that the statements Y < X and X < 2Y are false.

Assume that this is not true — that there are counterexamples X and Y such that the statements Y < X and X < 2Y are false.

Or vary your phrase as you suggested, or break it up into shorter sentences, or a combination of methods throughout the document. In this particular case, I got to "such that" and had to go back and read the first part again.

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I really like the dash. Are there any formal rules for its use, like for the colon or semicolon? So far, I have avoided the dash because I do not know how to use it. –  Greg Graviton May 23 '12 at 13:39
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In other words is a fairly standard replacement for i.e and that is.

In other words, I use that phrase whenever I wish not to use i.e or that is.

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