11

In the mathematics,

a < b

I think it should be said as "a is less than b"

So, does can I say the title ("a < b < c") as

b is larger than a and less than c

or is there a better way to say?

6
  • If you are asking this with the intent of clear communication to some other person or groups of people, you could combine several answers. Say one answer, then "in other words," then another answer. For example.
    – Phlarx
    Feb 13, 2020 at 17:33
  • Who is your audience? If you're talking to mathematicians, many of the answers below are ok if generally over-precise. If you're talking to non-mathematicians, many of the answers below are painfully inadequate.
    – Tony Ennis
    Feb 13, 2020 at 20:48
  • What about : "a, b, c are sorted in increasing order"? Feb 13, 2020 at 21:42
  • Related: I asked effectively the same question on SE Math Educators last month. To date there has been no consensus: matheducators.stackexchange.com/questions/17706/… Feb 14, 2020 at 1:40
  • 3
    I don't think I understand how this is opinion based. There may be variation among subgroups but that's not a matter of opinion.
    – Mitch
    Feb 14, 2020 at 2:48

9 Answers 9

12

In higher-level math, my experience says that a < b < c is usually pronounced as "a less than b less than c".

A large part of this is context. If we're examining the result of something, it's certainly possible that someone would say "b is between a and c", leaving some information out (that a < c). This is especially true where one or both of a and c are fixed, as in 2 < b < 7 ("b is between 2 and 7").

The most common case of a < b < c is when one is stating conditions, as "In the case a less than b less than c, we have...". It's easy to see why it's pronounced that way in this usage - we're naming the case we're referring to instead of talking about what the name of the case represents. Since we're just reading a name, we pronounce each character separately.

Note that the programming usage (the other place this might show up) is different: a < b < c would usually look like if a < b < c: and be read "If a is less than b is less than c...".

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  • 1
    @Mitch No. That's not the common usage. Feb 13, 2020 at 18:26
  • 3
    Leaving out the 'is' is much less common, and unnatural sounding.
    – Mitch
    Feb 13, 2020 at 18:30
  • 1
    @Mitch Not in higher math, which I was speaking to. In my experience, at least. Feb 13, 2020 at 18:39
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    My experience is that both phraseologies appear with reasonable frequency in higher math, with the is included in all other cases, including basic- and intermediate- level math. Feb 13, 2020 at 21:00
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    When you write on the blackboard teaching class, you say just like this.
    – Matsmath
    Feb 13, 2020 at 21:11
21

I would say “a is less than b which is less than c”. Just saying “a is less than b is less than c” is ambiguous about whether it’s a or b that is less than c.

7
  • 19
    “a is less than b is less than c” may or may not be ambiguous, but in the context of math, it is what is said.
    – jamesqf
    Feb 13, 2020 at 17:28
  • 2
    I don't know how you could parse the second to mean anything other than a<b<c. Can you clarify why you think it's ambiguous? Feb 13, 2020 at 20:48
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    @AzorAhai I think it's more unclear than ambiguous, but once the expression is familiar it's no longer unclear either.
    – Daniel
    Feb 13, 2020 at 21:31
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    @AzorAhai Consider the following (slightly longer sentence): "a is less than b, is less than c, and is greater than 0". That parses out as 3 simultaneous equations: a<b, a<c and a>0... It is then not entirely unreasonable to parse "a is less than b is less than c" (which is, regardless, grammatically incorrect) as a<b and a<c Feb 17, 2020 at 12:49
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    @Chronocidal I finally understood it, what helped me what parsing it as "a is less than (the difference between b and c)." So if b=10 and c=5, a<5. Thanks though Feb 17, 2020 at 18:22
9

There is many different way to say that. But, I think this is clearest way : "A is less than B and B is less than C"

6

I would just take it at face-value and read it left-to-right: "A is less than B is less than C."

0
2

I would say b is between a and c non-inclusive or, in the middle of a sentence a less than b less than c. (Yes, in a mathematical context I would not use the is.)

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    A matter of opinion, Mike. For me "<" means "is less than" in most cases, it makes for better English when you are reading the expression. The only cases where I wouldn't use "is less than" are when there is an element of assignment; for example "Let a be < b" or, preferably "Set a < b" which would be pronounced "Let a be less than b" and "Set a to be less than b". If I can't read algebra as normal English I can't follow it when it gets complicated.
    – BoldBen
    Feb 13, 2020 at 6:42
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    Why not “strictly,” instead of “non-inclusive”
    – cole
    Feb 13, 2020 at 19:45
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    This does not imply that c is greater than a, and thus does not capture the spirit of the original equation. It only says that b is between two other values, but we don't know which of those other two are larger.
    – Brian R
    Feb 13, 2020 at 19:54
  • @cole You certainly could -- I'm simply conveying what I, someone who has done a decent bit of math, would personally say. With strictly, I would have to say it twice, which ends up burying the lead. Feb 14, 2020 at 0:17
2

In fact, a more mathematically correct way to say that would be this:

a is strictly less than b and b is strictly less than c

The < symbol doesn't denote just inequity, but strict inequality.

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    Inequity is strict unless specified otherwise. This answer makes a statement which is already, of necessity, wordy, even more complex for no convincing reason. Feb 13, 2020 at 21:02
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    @RyanJensen I know that this is an old comment but: this is not necessarily true. A lot of analysts will use "less than" to mean the weak inequality. Indeed, Barry Simon makes this explicit in his five volume treatise on mathematical analysis. In most contexts, this distinction doesn't make much difference, but if the distinction does matter, then the answer here is spot on. Nov 18, 2021 at 12:13
2

Like all writing, I think this depends on who you expect to be the reader. If it were a purely math audience, you would not bother to use words.

1) a < b < c

would be enough.

If it a non-math audience, and the context was already established that a was less than c, then "b is between a and c but doesn't equal either" would be pretty clear.

If the audience was more visual than verbal, you could draw a picture of a, b, and c appropriate for the problem space.

Everything about words depends the writer anticipating the interpretation by the reader, without becoming too words or pedantic.

Simple sentences to convey simple ideas. Sentence fragments, even.

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  • While a good answer for a written style, this is bad for a verbal or spoken style, such as a teacher talking to a class Feb 17, 2020 at 12:54
  • @chronocidal, your comment is spot on. Checking back to the question, the OP asked about "is there a better way to say". I took that to be a an informal word for "write", but he wrote "say".
    – cmm
    Feb 17, 2020 at 13:12
-1

I would say "b is strictly between a and c", or if it's very clear from context or the distinction with a ≤ b ≤ c doesn't make a difference (e.g. in case of a continuous probability) just "b is between a and c". I would consider the latter way of saying it much more conventional however.

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    However "b is (strictly) between a and c" doesn't tell you anything about the relationship between a and c (i.e. a < c). Feb 13, 2020 at 13:05
  • I'd say it's quite customary that a is the smaller and c the larger value when saying "between a and c"
    – Tomlish
    Feb 13, 2020 at 13:13
  • Also in non-mathematical speech, e.g. "between 10 and 12 grams of flour" or "I'll be there between 8:30 and 9"
    – Tomlish
    Feb 13, 2020 at 13:16
  • 3
    If the equation was a>b>c, how many people would say that "b is between a and c" isn't true? Feb 13, 2020 at 14:52
  • I can't imagine a context where OP's statement isn't intended to be strictly true mathematically. This suggestion says something that's not equivalent.
    – jimm101
    Feb 13, 2020 at 16:26
-1

Taking your second quote, which lists both a and c with respect to b, you can rearrange it slightly:

a is less than b, and c is greater

2
  • so is c greater than a or b?
    – Kevin
    Feb 13, 2020 at 21:31
  • @Kevin Yes. However, due to the way that the English language functions, the implicit object of the second part of the compound sentence is the same object as the first part of the compound sentence: in this case, b (with both a and c being the subjects). We do not need to repeat "than b" - that would be redundant, and thus bad grammar Feb 14, 2020 at 0:40

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