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When I read a math textbook, I encountered:

The condition that a function be continuous is...

I don't know why I need to use "be" instead of "is".

Is it inappropriate if I use "is"? Is there any other word other than "condition" that I need to use "be"?

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    It is an example of the subjunctive mood. "... the form of the present subjunctive verb used to express present or past desires .."
    – Robusto
    Jan 3 '17 at 2:06
  • I think you could use "is"; however, the author may have thought that using is twice within a three-word span sounded awkward: The condition that a function is continuous is...
    – J.R.
    Jan 3 '17 at 2:26
  • It's very common in math to say "Let N be an integer..." "Let f(x) be a function such that...". The author has turned this around somewhat awkwardly
    – John Feltz
    Jan 3 '17 at 2:29
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    It's not awkward at all. It is subjunctive mood. It's almost like saying "The condition that a function should be continuous ..." where should expresses a desired state.
    – Robusto
    Jan 3 '17 at 2:38
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    @Rob I don't think desire quite fits. It's not clear that the speaker feels desire. The unfortunate condition that a function be continuous prevents us from applying the simpler theorum in this case. Jan 3 '17 at 3:27
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We could use is to communicate essentially the same idea:

The condition that a function is continuous is (some declaration).

The reason you question the use of be in the fragment is likely that it is an example of a use of the subjunctive mood, which is an often invisible feature of English.

We use the subjunctive to talk about things that are more like mental ideas than factual realities. Dividing utterences into these two categories is often a tricky enterprise.

That a function is continuous is put forth as more of an idea than a factual reality. The idea is issued as a supposition, and we can use the subjunctive mood to communicate such an idea, though we do not always need to.

The subjunctive is often in operation but not noticeable, because in English the subjunctive often appears identical in form to the indicative mood, which (perhaps we can say) more plainly or ordinarily refers to "real", more tangible things.

I will borrow description and examples from the current Wikipedia article on the English sunjunctive, located at:

https://en.m.wikipedia.org/wiki/English_subjunctive

Consider:

He sees a doctor once a year.

This is an example of a use of the verb see in the indicative mood. As you likely expect, see is inflected to sees because it's used with the third-person singular, he.

Compare to:

It is important (that) he see a doctor immediately!

The idea here is different because it describes an opinion or idea that exists in the speaker's mind, not an action or event that we can find in the real world.

Because the subjunctive is in use, we do not change see to sees.

In

It's important that they see a doctor immediately!

We might say that the subjunctive is likely in use because it is likely an opinion or belief, but the form is the same as if it were a use of see in the indicative. In this rather common situation, the operation of the subjunctive is not visible.

Since verbs in the subjunctive appears in unexpected forms only in certain situations, it can surprise and puzzle learners.

One of the ways that the subjunctive appears as noticeable in form is with use of the verb be.

In the example you encountered, be is not changed to is because the grammar of the subjunctive mood differs from that of the indicative.

Yes. There are other verbs with which we use be in the subjunctive and where be does not change form as in the indicative:

I suggest (that) he be taught some manners.

I demand (that) she be promoted.

If that be the case, we should leave.

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  • Nice explanation. I've learned something today.
    – Mick
    Jan 3 '17 at 4:59
  • +1 This should be the accepted answer subjunctive indicative mood since it is a statement of fact and the definition for continuous functions is well known and well defined.
    – Peter
    Jan 3 '17 at 7:36
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This may not exactly answer your question specifically on why be is used, but specific jargon may sometimes not be perfect English, consider all the posts on headlinese or song lyrics but they will be perfectly understandable given the surrounding context. Your question is about English grammar when applied to maths, so it's a very left-brain, right-brain combination and you may want to consider that when ruminating about the answers being given.

Here is a link to the maths syntax precedent, maybe it might help in your understanding.

The simple reason be is used instead of is is because there is a

formal syntax for mathematical proofs

which uses {let, be} as part of the syntax see Section 11.2 and not is.

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  • Sorry, that's not it.
    – Robusto
    Jan 3 '17 at 2:39
  • Are you saying it's different than "In order to be a US national, a person needs to..."
    – Peter
    Jan 3 '17 at 2:53
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    @Pet I think you are wandering in a logical wilderness lost; not that I'm necessarily on the perfect track myself. And anyway, adventures in Wonderland can bring all sorts of value. Your teacher can say I'm hungry without first contemplating which mood s/he will employ in the expression, and that would not prohibit us from making observations about the grammar of the utterence to explain probably why s/he didn't say I is hungry. Jan 3 '17 at 4:47
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    @JimReynolds +1 A man who understands the value of becoming lost. It was my rambling way of answering the OP's "why": "it's that way because it is" as is much the case with language. Not sure why I got all existential maybe because it's the new year, but thank you, one of the nicest compliments I've received on this site. All the best in 2017!
    – Peter
    Jan 3 '17 at 7:15
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    I would +1 yours if it said something like "This might not exactly explain why be can be used here, but it may be useful to look at some similar uses and think about how they might be connected," or something like that. I am willing to upvote anything that I think might help OPs and other readers take any kind of step in what seems to me a useful direction. I think you sort of did that by saying "The simple reason". Jan 3 '17 at 7:41
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The condition that a function is continuous is....

The condition that a function be continuous is....

Both the sentences are grammatical, with a slight difference in meaning.

The former expresses the condition that, in fact, makes a function continuous. It's a declaration of facts. In grammar, you say that the verb "is" in the indicative mood.

The latter expresses the condition in a hyothetical or suppositional manner, which may make a function continuous. Grammatically speaking the verb "be" is in the subjunctive mood.

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