Grammar Question: Should "then" be used in mathematical statements?

[Fredrik]

I'm not sure what forum to put this in. Moderators, feel free to move it if you think it belongs somewhere else.

I've been reading some documents on how to write good LaTeX documents, and one of them claimed that the phrase "If A, then B" is incorrect in English. According to that author, you should either write "Suppose A. Then B." or "If A, B". For example, "If x is a member of X, f(x) is a member of Y" is OK, but "If x is a member of X, then f(x) is a member of Y." is not. That sentence certainly sounds better without the "then", but what about a sentence with more math symbols and fewer words? For example:

$$\text{If }\{x_i\}_{i\in I}\text{ is a net in A and }x_i\rightarrow x\text{, }x\in\overline A\text{.}$$

Wouldn't it be OK to add a "then" for clarity? I mean, a comma often means "and". I don't think this one will be misunderstood, but won't it make people go "uh that looks weird"?

 

[CRGreathouse]

Using "then" is fine. I use a comma when it's clear and break it up (with "then", other words, or a sentence end) otherwise.

 

[hamster143]

http://dictionary.reference.com/browse/then

"if .. then" combination appears to be valid.

 

[rs1n]

http://en.wikipedia.org/wiki/Conditional_sentence

 

[Rasalhague]

The combination "if P, then Q" looks perfectly okay to me as a native speaker of (British) English, just as grammatically correct as "if P, Q". As you say, it's useful for the sake of clarity to add "then" when the subordinate clause ends in a symbol, and the main clause begins with a symbol. I've never even heard of a stylistic rule against "if P, then Q", let alone a grammatical one, and it seems to be common enough, between words or symbols:

"If $(a,b) \enspace \in \enspace >$, then $a > b$" (Nakahara: Geometry, Topology and Physics).

"If x - y = x' - y', then x - x' = y - y' " (Bowen & Wang: Introduction to Vectors and Tensors).

"If that worldline consists of the events (t,$\zeta$) in the Greek coordinate system, then the velocity of the particle is $\sigma = \Delta \zeta / \Delta \tau$, according to G" (Callahan: The Geometry of Spacetime).

"If $\alpha$ is not given a value, then $x^\alpha$ is any of the four components" (Schutz: A First Course in General Relativity).

I have seen it stated that a subordinate clause before a main clause should end in a comma, and follow this rule myself, although it's often ignored, especially when the sentence consists mainly of words:

"If A precedes B then a light ray leaving A at the moment A occurs will arrive at B as B occurs" (Adams: Relativity: An Introduction to Space-Time Phyics).

 

[Studiot]

Surely this is a matter of personal preference.

No one has a patent on the grammar of the English Langauge - such an attempt has been an abject failure in French.

One of the great strengths of English is that it is a vibrant, live language that is still developing. Another is that there are often many ways to phrase the same thing.

(Aside - there are two clauses in my last sentence, which is the subordinate and why is it bad to have a separating comma?)

If you made a rule in English Winston Churchill could always find an exception!

Finally, I agree with Rasalhague. The 'then' often adds clarity. Particularly in the situation not yet mentioned

The 'If...then...else' construction.

 

[Rasalhague]

Another is that there are often many ways to phrase the same thing.

(Aside - there are two clauses in my last sentence, which is the subordinate and why is it bad to have a separating comma?)

Here you have a main clause (synonym: independent clause) consisting of the verb "is", its subject "another" and its object, a clausal complement "that there are often many ways to phrase the same thing" (i.e. a clause which is the complement of the verb "is"). In English, there wouldn't normally be a comma before "that" in such a sentence, and prescriptive grammars don't recommend one, as far as I know. It's not bad for any reason; it's an arbitrary rule/tradition, just like the rule that there should be a comma in German.