Suppose a sentence such as

Let X := a and Y := b, that is X is foo and Y is bar ..

Is this correct english? I try to first a give a formal mathematical definition of X and Y, and then repeat the same in an informal way. I would use "that is" to link the second sentence to the first one.

  • 1
    I was about to comment when someone downvoted. However, I'll carry on. I'm not sure that Let X := a is standard maths terminology; I'd expect Define XϵN: X = Y + Z, for example. As an 'English' example, you'd want at least a semicolon between the statement and the explanatory echo. McGonagal is an animorph but Lupin is a werewolf: that is, McGonagal can elect to shift shape, but Lupin is constrained to under certain conditions. Jul 20, 2015 at 11:57
  • @Edwin *McGonagall. ;-) Jul 20, 2015 at 12:07
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    @Edwin: Let X := a has been used in some math papers, although it's relatively uncommon and I suspect it's taken from programming languages. But it is used often enough that people should understand it. And the standard advice is to punctuate math as if it were English, so you really do want a semicolon there. (There are times when punctuating math like English gives horrendous results, so you have to make exceptions; these are quite rare, though.) Jul 20, 2015 at 12:11

1 Answer 1


"That Is" is a common idiom that means "in other words"

From http://dictionary.reference.com/browse/that?s=t

  1. that is, (by way of explanation, clarification, or an example); more accurately:
    I read the book, that is, I read most of it.
    Also, that is to say.
    I believe his account of the story, that is to say, I have no reason to doubt it.

The only problem with the quoted sentence that I can see is the punctuation: there should be a semi-colon before "that is" and a comma after it:

Let X := a and Y := b; that is, X is foo and Y is bar

(If := is the way you really want to express 'equals'. A simple equals sign is the usual way.)

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    From Whitesmoke: '1. Use a semicolon [ / colon / dash] between two independent clauses linked by either a conjunctive adverb or a transitional expression (“in addition”, “for example”, “on the one hand”, “nevertheless”, “in other words”, “namely”, “meanwhile”, “in fact” [etc]) when in the middle of a sentence, between the clauses....' [bolding mine] >> I read the book – that is, I read most of it. Jul 20, 2015 at 12:02
  • @EdwinAshworth Thank you. I'm happy for that to be the authority on the usage (although my anti-virus does not like Whitesmoke). Edited to include that.
    – Avon
    Jul 20, 2015 at 12:22
  • There are many more readily recognisable authorities proscribing the comma splice. There are even one or two that sanction its use in certain limited contexts (a search on ELU would probably lead to the discovery of at least one). Jul 20, 2015 at 12:31
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    X := a is the standard way to say X is defined ... in symbols rather than words. I think here the OP is simplifying their question (which is not a math one). The actual maths could be something like X := {x : x >0}.
    – antonio
    Jun 28, 2017 at 14:35

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