Replacements for "i.e." other than "that is"
What about namely?
Assume that this is not true, namely, that there are counterexamples X and Y such that the statements
Y < X
andX < 2Y
are false.Assume that this is not true--namely, that there are counterexamples X and Y such that the statements
Y < X
andX < 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.
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
andX < 2Y
are false.Assume that this is not true, that there are counterexamples X and Y such that the statements
Y < X
andX < 2Y
are false.Assume that this is not true — that there are counterexamples X and Y such that the statements
Y < X
andX < 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.
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.