By NeutronStar

2019-01-10 16:35:54 8 Comments

This question, "Discrete Units of a Continuous Quantity", asks whether units of a continuous quantity should be spoken of as discrete or continuous.

The top answer states

The rule is simple, and you obviously know it: discrete quantities require the use of "fewer" and continuous quantities require the use of "less".

Calorie, as a unit, requires the use of "fewer". Energy, as a continuum, requires the use of "less".

"Fewer calories means less energy."

I do not understand the logic here though. Calorie is a unit, yes, but it is a continuous unit (it is possible to have half a calorie, or 4.582394 calories). Since a calorie is such a small unit of energy compared to what it is usually used for (food energy and human metabolism), it is very seldom expressed in a fractional form and instead is rounded (usually to the nearest 10 or higher).

Why then should "fewer" be used with calorie instead of "less"? Is there another relevant rule than just "continuous quantities use "less" and discrete quantities use "fewer"?


@Stathis Avgoustiniatos 2019-01-13 07:44:56

In expressions like "less than ten minutes", "less" is correct because it could be considered as referring to the implied word/concept "time", as in "less [time] than ten minutes". The emphasis is not in the units as the exact quantity of time in non-integer (in general) minutes is not important, as long as it is less than ten minutes. So for continuous quantities, as energy, time, and distance, I consider both "less" and "fewer" to be technically correct, with "less" being better. When someone refers to something discrete, as in "ten free throws or less", I would consider "less" to be technically wrong but it still sounds good to me. Just as when adjectives are used instead of adverbs.

@user329850 2019-01-13 00:06:30

Both less and fewer are correct, however, many English speakers prefer fewer in this context, especially in formal speech. Here's the relevant portion from the Cambridge Grammar of the English Language, Chapter 13, Section 4.1.2:

The relation between less and fewer is fairly complex. In non-count singulars only less is possible: Kim has less/*fewer money than Pat. In plural NPs we have:

  1. She left less than ten minutes ago.
  2. Less/Fewer than thirty of the students had voted.
  3. He made no less/fewer than fifteen mistakes.
  4. You pass if you make ten mistakes or less/?fewer.
  5. He took less/*fewer pains to convince us than I'd expected.
  6. He made fewer/less mistakes than the others.

Both [1] and [2] have than + numeral. In [1] ten minutes expresses an amount of time rather than a number of individuated units, and in such cases fewer is virtually impossible – just as few would be in a comparison of equality: She left as little/*few as ten minutes ago. Similarly with We paid less than thirty dollars for it; She's less than forty years old; We were going at less than ten miles an hour. In [2] we are concerned with countable individuals and little cannot be used in a comparison of equality (*as little as thirty of the students); nevertheless, for inequality less is more common than fewer in this construction. The same applies with percentages: Less/Fewer than 30% of the students had voted. Construction [3] has the comparative form following no: though the interpretation is count plural, less is here again more common than fewer. Construction [4] has or after a numeral: less is the usual form here, with fewer quite marginal; this construction is widely seen in supermarkets, with the fast checkout labelled eight items or less, or the like. In [5] pains is plural but non-count rather than count (we can’t ask how many pains he took), and here only less is possible. Finally in [6] the comparative occurs directly with a count plural noun: both forms are found, but less is subject to quite strong prescriptive disapproval, so that fewer is widely preferred in formal style, and by many speakers in informal style too. [emphasis mine]

[Quotation edited for formatting/readability.]

So the short answer is that the traditional rule is an oversimplification, but it has influenced English speakers to prefer fewer over less in this context. But nevertheless, both forms are found and are thus not wrong.

@vectory 2019-01-12 06:02:21

We simply don't speak of 5 Energy.

The key difference here, mathematically, is rationals vs real numbers. That is, even if you cut your kilocalories in half, you would always have a finite-length number to describe the amount. Hence, the rationals as well as the natural numbers are called countable. The set of Real Numbers on the other hand is an uncountable set, because for every finite-length number, you can have an infinite amount of infinite-length real numbers that start with the finite length number. The details are tricky, I'm not a maths teacher.

So far so good. Why then is energy uncountable? It's a historically grown thing. The whys and hows of this fact should be part of a different question, though. (I mean, I really don't know).

Suffice to say that the distinction between the measured object and the measurement result is purposeful.

@stewbasic 2019-01-14 05:39:52

I don't think this distinction is relevant. The set of numbers we can name in the English language is countable, so this argument would imply we should always use "fewer" rather than "less".

@JiK 2019-01-15 15:06:48

Also, it seems this answer is somehow confusing the mathematical idea of countable or uncountable sets and the linguistic idea of countable and uncountable nouns.

@vectory 2019-01-15 15:14:49

@JiK it's not confusing, it's trying to combine or, rather, ameliorate, consolidate, subsume. I think the concepts are easy enough not to be confused. I have to concede to stewbasic, that while PI is a real and a computable number, thus easily named, the computable numbers are still countable (in the logic sense) and I wouldn't know a theme to name or enumerate (same difference?) an uncountable set. I can easily name the set, though.

@vectory 2019-01-15 16:04:43

@stewbasic there's a school of constructive mathematics that tries to work from the computable numbers, avoiding the uncountable set of real numbers. Implying that continuities like one likes to imagine could be done away with. For Grammar, it's an interesting question and some problems are immediately obvious (much sand vs many sands) other's are problematic anyhow (many calories vs many (types of) calories vs much fruit vs many fruits) and there are cases where, if you need to demark a grammatically countable set as practically uncountable, you suddenly have some problems.

@David Richerby 2019-01-11 23:45:32

it is possible to have half a calorie, or 4.582394 calories

It's also possible to have half a cow or 4.582394 cows. Indeed, the same is true for almost every countable noun that existed at the time when "fewer" came to be the word we used with countable nouns. Perhaps it's impossible to have half a thunderclap...

This shows that it's a mistake to think that the existence of fractional quantities means that a noun is uncountable. Rather, countable nouns are those that can be modified by a number and which have singular and plural forms.

@PatrickT 2019-01-12 18:32:24

Are we talking about Schrodinger's cow?

@Sean 2019-01-12 21:22:01

@PatrickT: No, that's when we simultaneously have one cow and no cows.

@MichaelK 2019-01-14 10:00:03

@PatrickT No, we are talking about the Spherical Cow.

@PatrickT 2019-01-14 12:45:46

And we'll know which it is only if we open it up, right?

@Barmar 2019-01-11 16:57:14

While calories are continuous to scientists, most lay people don't think of them that way. Food and activity calories are always reported in whole numbers, often only precise to hundreds or thousands, because for most people's purposes any more accuracy is not meaningful or useful.

So in common use we treat them as discrete units, and the language we use reflects that. We use "more" and "fewer" when comparing things, and ask things like "How many calories does an egg have?" and "How many calories do does an hour of exercise use?" (rather than "How much", which would be used for non-countable quantities).

@michael.hor257k 2019-01-11 20:08:21

I don't think "calories are continuous to scientists". Energy is continuous, the units that measure it are not. The problem is that with energy, we often use the units to speak about the quantity. We say how tall is the building, not how many meters is the building. We ask how much do you weigh, not how many pounds do you have - but we ask how many calories are in this snack when we mean how much energy is in this snack.

@Barmar 2019-01-11 20:18:16

@michael.hor257k Yeah, it's hard to describe the precise thought processes, I was just trying to convey that regardless of how it might be treated technically by scientists, that's not how lay people talk about it. I'm also reminded that in French they use similar terminology for age, they ask "How many years do you have?"

@PLL 2019-01-12 01:17:35

To sum up the point briefly: Scientifically, calories are continuously divisible (or at least the quantity they measure is), but grammatically they’re countable, and that’s what’s relevant for the fewer/less distinction.

@michael.hor257k 2019-01-13 05:31:48

@PLL To reiterate the point, calories are not "continuously divisible" - scientifically or otherwise.

@Barmar 2019-01-13 05:38:18

@michael.hor257k Unless you're talking about the quantum level, they're as continuous as any other scientific measurement.

@michael.hor257k 2019-01-13 05:42:24

They are units, not measurement. Units are not divisible, and certainly not continuously.

@Barmar 2019-01-13 05:50:12

@michael.hor257k You can't have fractional calories?

@michael.hor257k 2019-01-13 11:20:46

Please separate the value from the units. Think a form with two cells, one for quantity and one for units, e.g. "| 123 | kg |" or "| 4.56 | cm |". Now do you see my point? Values are fractional, units are not. And values expressed as decimal numbers are not continuously divisible - but that's another story.

@Barmar 2019-01-13 22:43:36

@michael.hor257k I don't think that's a useful distinction. We think of the amount and units together as the description of a quantity. The only question is whether the quantity comes in discrete units (like balls) or is something continuous (like distance). And in between there are things that are units but can be split up, like cookies.

@michael.hor257k 2019-01-13 22:56:59

I think it's an immensely useful distinction - and I am not the only one:

@Barmar 2019-01-14 01:33:12

Maybe in some contexts, I don't think it's important when discussing the way the term is used in non-technical contexts.

@user331579 2019-01-11 16:32:51

I think the citation you provide is misleading because it refers to the intrinsic qualities of the thing described by the noun.

My suggestion: Don't focus on whether a noun refers to something divisible. (Virtually everything is divisible.) Instead, just research to find out if a word is "countable" or "uncountable".

Sometimes, words will function both ways -- three beers are countable, while "some" beer is not countable. If you say, "I would like a lot of beer," the listener might bring you a single large keg of beer, but if you say, "I would like a lot of beers," the listener will bring you many cans or bottles.

In short, don't think too hard about it, just look up the word you have a question about in the English learners' dictionary:

@Zebrafish 2019-01-10 21:49:25

You shouldn't use "fewer" instead of "less" necessarily. Look at this NGram:


In many cases "less calories" is more common than "fewer calories". In no case is there an enormous difference either way.

It depends on how conceptually you see what it is you're describing with either "less" or "fewer". In this case it's whether you see the calories as individual units (plural), or one sum of things, ie., energy (singular). Oxford Online Dictionary blog explains:

(In a supermarket/store) Ten items or less.(Correct or incorrect?)

Firstly, having absorbed the guidelines above, you may suppose that some supermarkets are grammatically on the ball by displaying notices at checkouts that state ’10 items or fewer’ (fewer rather than less being the right choice because it’s referring to items, that is, a number of things?). In fact, there were reports a few years back that Tesco had replaced their signs reading ’10 items or less’ with ones which said ‘Up to 10 items’, so as to placate the sticklers. Sorry, no need! This is an example of hypercorrection. Pocket Fowler’s Modern English Usage puts it very succinctly:

  • ‘Supermarket checkouts are correct when the signs they display read 5 items or less (which refers to a total amount), and are misguidedly pedantic when they read 5 items or fewer (which emphasizes individuality, surely not the intention).’

The point is fewer is used for plural and less for singular. But the mental notion of whether something is singular or plural seems to be an influencing factor in whether "less" or "fewer" is used.

Look at the difference in usage between:

  • less than two miles
  • fewer than two miles

The full explanation of "fewer" and "less" is not just as simple as the explanation in the answer you linked.

@Apollys 2019-01-10 22:52:02

"Less calories" is definitely wrong, as you have explicitly demonstrated "calorie"'s countability by writing it in its plural form.

@Zebrafish 2019-01-10 23:25:14

@Apollys Are either "less than ten items" or "ten items or less" wrong also?

@Zebrafish 2019-01-10 23:49:09

@JohnMontgomery So you disagree with the writer of the Online Oxford Dictionary article, Pocket Fowler’s Modern English Usage, along with other grammars, and CGEL that characterises your insistence on this as a "shibboleth" and "stylistic choice". OK. It's strange, because "I'll be back in fewer than ten minutes." doesn't quite sound right.

@Oscar Bravo 2019-01-11 08:01:01

less than ten minutes is correct because the focus is on the the thing that is less than ten minutes. You are really saying, I'll be back in a time that is less than 10 minutes. The time you are talking about is continuous so can be less than a fixed time. If you say 10 items or less, you are talking about a group of items that can be counted and that can be fewer than ten. You've switched the focus of the statement.

@Especially Lime 2019-01-11 09:16:34

@OscarBravo If you say "10 items or less", it's not really clear what you are talking about because you have elided the word that "less" qualifies. A lot of people use it to mean "10 items or less stuff", which is why "less" sounds natural. On the other hand, it doesn't make quite as much sense to view "10 items or fewer" as an elided form of "10 items or fewer items", because the latter would more naturally be expressed as "10 or fewer items".

@Apollys 2019-01-11 22:21:27

Less than 10 minutes could be any amount of time smaller than 10 minutes. Fewer than ten minutes makes it sound like you can only arrive it integral numbers of minutes which is very strange As Oscar said, the meaning is: I'll be back in an amount of time that is less than 10 minutes.

@Apollys 2019-01-11 22:26:12

@Zebrafish In the case of items in a grocery story, since you must buy items in whole number quantities, those other examples are wrong. In the case of calories, which may exist in portions, it's fine to say "less than X calories" or "X calories or less". So it seems my original justification was incomplete.

@alephzero 2019-01-12 00:53:31

@Zebrafish If you are talking about groceries, don't you mean "ten item's or less?" ;)

@Zebrafish 2019-01-12 03:05:02

@alephzero I'm not sure what you mean by "item's". Maybe items'? I'm open to multiple possibilities. "ten items or less", "ten items' (worth) or less", "ten items or fewer (items)". I see this as a notional agreement issue, where for example both "The group are" and "The group is" are both acceptable. This seems to be particular to "fewer" and "less", which is why I think it causes confusion (myself included) and why Wikipedia has an article devoted specifically to these two, because it's contentious. It pops ups in other areas too, like NGram search for "two gallons was/were"

@livresque 2019-01-12 08:10:19

@alephzero It's "ten items our less."

@tungsten_carbide 2019-01-11 02:49:46

"Fewer" refers to quantity in general, even when the notion of units is ambiguous or abstract. It can refer to discrete, continuous, and even infinite quantities.

There are fewer points in the Cantor Set than on the closed interval [0 ... 1]. Note that both sets of points are infinite, but the Cantor Set is a lesser infinity.

There are fewer kilometers to travel from Earth to the Moon than from Earth to Mars on any minimal-energy trajectory. If the journey is powered by conventional rocket propulsion systems, the engines will burn fewer calories, and proportionally fewer Watts. Also note that at the end of that last sentence, Grammarly suggested I use "fewer."

There are fewer odd numbers than integers in the set of whole numbers ranging sequentially from 1 to any fixed positive integer N greater than 1.

Why? Because this is English.

@MarkTO 2019-01-10 17:14:23

Divisibility does not mean something is not countable or that it isn't a discrete unit, requiring use of 'fewer'. A calorie is not 'energy' it is a 'unit of energy', and therefore, countable and discrete, even though it's divisible. It's divisible into further discrete units - half a calorie, in this case, is still a discrete unit.

Using another example, you would have 'fewer' jars of peanut butter, even though someone might have eaten half of the peanut butter in some of the jars. You could even cut the entire jar in half, none of that matters, you still have fewer jars. And you also have less peanut butter, in the same way that fewer calories means less energy. The calorie corresponds to the jar, not to the peanut butter (that would correspond to the energy the calorie measures).

It doesn't matter that there is 'less' peanut butter in some jars than in others any more than it would matter if some of the jars were a gallon in size, and some were just single-use jars with two tablespoons of peanut butter inside. Put another way, your 'half a calorie' is still a unit, and thus, you'd still say 'fewer calories'.

@supercat 2019-01-11 00:47:37

Some units are used as synonyms for the quantity being measured. In formal writing, this is generally only done with a few nouns that have an "-age" suffix (for example, people usually refer to "voltage"), but informally it may be applied to a wider range of units. When describing "X as having "50% less calories than Y", the word "calories" is shorthand way of saying "caloric energy" using 50% fewer syllables.

@1006a 2019-01-11 00:55:01

I don't think your jar analogy is working here, especially the discussion of jars that are half-empty (even though we talk about "empty calories", it's not really possible for a single calorie to contain less energy than any other calorie). Maybe tablespoons of peanut butter would work better?

@Lawrence 2019-01-11 01:55:18

@1006a This is one of the rare times I disagree with you. The jars and peanut butter work deliciously. (Except perhaps when the jars are cut: 1.5 jars doesn't sound like it should be described as "fewer jars" than 2 jars; but "less jars" sounds worse.)

@Janus Bahs Jacquet 2019-01-13 02:17:20

@supercat I doubt that is what’s going on in most cases. It’s more likely just that the distinction between less and fewer is becoming blurred in English, and a lot of people use less almost exclusively. Many also say ‘less people’ and ‘less units’, neither of which can be explained as any kind of shorthand. And hardly anyone, even if they otherwise distinguish less and fewer, would say, “There are fewer than ten minutes left” – fewer still would even begin to consider, “There were more or fewer a dozen people in the room”.

@568ml 2019-01-13 12:38:47

@JanusBahsJacquet indeed so: in conversation with my barber not long ago I used the word fewer and he stopped me to ask what it meant.

@wizzwizz4 2019-01-13 18:34:44

@Lawrence There's less jar (less jar-stuff).

@Lawrence 2019-01-14 01:10:05

@wizzwizz4 That uses jar as metonymy for the stuff inside. If they want to refer to the jars themselves, “less jar” sounds a little jarring.

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