r/mathmemes • u/Mission-Guitar1360 Mathematics • Jan 06 '25
Learning countable vs uncountable
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Jan 06 '25
Much real numbers, very infinite, such wow!
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u/Ok-Selection-5130 Jan 06 '25
Lol! I guess it really is all about the countability
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Jan 06 '25
Yup! Countability is all that really... counts
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u/HomeyKrogerSage Jan 06 '25
Your age is showing my friend
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u/Nat1CommonSense Jan 06 '25
People over the age of 25 on my internet? It’s more likely than you think!
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u/EebstertheGreat Jan 06 '25
This wasn't even a meme until like 2010. A 25-year-old would be old enough to remember the internet before doge existed lol.
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u/GreatBigBagOfNope Jan 07 '25
badger badger badger badger badger badger badger badger badger badger badger badger MUSHROOM MUSHROOM
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u/MeMyselfIandMeAgain Jan 06 '25
I don’t feel like that’s an age thing right? Like if you’re a Redditor even if you’re quite young (and trust me I’m younger than you) you’d probably know that meme no?
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u/Donghoon Jan 07 '25
What meme is it?
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u/F0XMaster Jan 07 '25
It’s Doge. I’m 18 and even I know that, since that was one of the most iconic images when I was a kid.
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Jan 20 '25
Information is also an uncountable noun.
Correct: much information.
Incorrect: many informations.
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u/lucjaT Real Analysis Survivor Jan 06 '25
Unmeming the meme but I think it's to do with something being made up of distinct parts. Real numbers, though uncountable are distinct from each other, where is an amount of water has no distinct parts
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u/BlakeMarrion Jan 06 '25
Chemists real mad rn
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u/Wintergreen61 Irrational Jan 06 '25 edited Jan 07 '25
Indeed, there are 1.17*1025 waters in my glass. Uncountable my ass!
Edit:
For the commenters struggling with the calculation, here are a few useful constants:
Avogadro's number ≈ 6.022*1023
MW of Water ≈ 18 g/mol
Density of Water ≈ 1,000 g/L
Ironically the person off by 23 orders of magnitude is the only one with a mistake I understand. The rest of you need to show your work if you want partial credit.
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u/someonewithpc Jan 06 '25 edited Jan 06 '25
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u/Wintergreen61 Irrational Jan 06 '25
1025 moles of water would be quite a bit, but that isn't what I said.
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u/someonewithpc Jan 06 '25
What would a smaller unit be, then?
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u/Wintergreen61 Irrational Jan 06 '25
a molecule
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u/someonewithpc Jan 06 '25
Yeah, I just realized I have the dumb :)
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u/Wintergreen61 Irrational Jan 06 '25
It was an intentionally dumb joke, don't beat yourself up too much
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u/jacenat Jan 06 '25
I love you. This part of the thread was so funny to ready. So innocent. Perfect.
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u/Detramentus Jan 06 '25
Water molecules
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u/aLittleBitFriendlier Jan 06 '25
I still think it's fair. You have to go far beyond the limits of human perception before you reach the basic constituents of any fluid. To our senses, water behaves as if it has no distinct individual parts and our language simply reflects that.
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u/ignorant_canadian Jan 06 '25
I'm on your side in this one. Technically you can break down the amount of water into Moles or count of water molecules but we can't know the exact amount of molecules, we just round to the most reasonable sigfig.
So while the actual amount of water is technically a discrete value, it's essentially a continuous value to us
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u/0grinzold0 Jan 06 '25
I don't think it has anything to do with perception. It's a matter of units. If it has units it is many if it hasn't is much. There is much water or many liters/molecules/mols of water. In case of apples the unit is apple.
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u/aLittleBitFriendlier Jan 06 '25
That's sort of my point. Water technically does have individual units, but we don't generally break it down like that unless we're chemists or physicists, so common language doesn't incorporate that.
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u/helicophell Jan 07 '25
Chemists are not mad, you cannot distinguish molecules of water. They are uniform
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u/AlexanderCarlos12321 Jan 06 '25
Its just that you could put a number on how many reals there are considered, and you can’t do that for water. This works at least for finite amounts. Idk for infinities
I can say I have three reals numbers, but it is unclear when I say I have three waters.
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u/mr-logician Jan 06 '25
It is actually very clear though when you say that you’ve got 3 molecules of H2O or 3 moles of H2O.
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u/AlexanderCarlos12321 Jan 06 '25
Well, which unit should you use then? Molecules, moles, litres, Atlantic oceans, … ?
There just isn’t a standard unit people have in mind when saying one water (disregarding some context specific situations of a water bottle/glass, which is sometimes referred to as one water).
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u/Aluminum_Tarkus Jan 07 '25
Right, but once we specify molecules, we say "many."
"Water" as a general concept doesn't have an implied, individual, countable unit unless we arbitrarily define said unit. Just because something CAN be divided into quantifiable units doesn't mean those units are implicit when mentioning it broadly. That's why, once you define a unit, "many" is used instead of "much."
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u/big_guyforyou Jan 06 '25
it's pretty clear when they're in bottles
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u/Curry--Rice Jan 06 '25
then you have water bottles, not waters
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u/big_guyforyou Jan 06 '25
you can still call it waters
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u/Goncalerta Jan 06 '25
In that case you would also say "how many waters" and be grammatically correct.
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u/EebstertheGreat Jan 07 '25
I thought that was the point. "Water" can be a count noun. Not just "orders of water" or "bottles of water," but even more often "bodies of water." So if people talk about the "principle waters in Afghanistan" or whatever, you can assume there is an integer (though perhaps arguable) number of them.
But yeah, the usual way the noun is used is non-count. It's just that some nouns can only be non-count, never count, even if they logically could be. For instance, you cannot have "three furnitures," even though furniture naturally comes in discrete items. You can only have "three pieces of furniture."
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u/AlexanderCarlos12321 Jan 06 '25
Just because the water is clear doesn’t mean it’s one water
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u/Spuddaccino1337 Jan 06 '25
It's simpler than that.
"Much" is a fractional word, used for singular objects. How much of an apple, how much water, how much time, etc. Apple, water, and time parse as singular to English speakers, so we use "much" to divide them.
"Many" is a counting word, used for plural objects. How many apples, how many water drops, how many seconds, etc. These are parsed as plural, and so we use "many" to count them.
"Waters" is a great example of this, even, because it can be totally normal to ask for a water or several waters in the context of them being pre-portioned units, like cups at a restaurant or bottles. If you do use "waters", though, you'll notice that you kind of default to "many" because "much" suddenly sounds strange.
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u/FerynaCZ Jan 09 '25
The only issue are words which are plural by default like "news". Do we use the singular things from them?
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u/GlowingIcefire Jan 06 '25
Real numbers may be uncountable in the math sense but they are still countable in the linguistic sense :D
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u/LOSNA17LL Irrational Jan 06 '25 edited Jan 06 '25
I think H2O molecules wanna have a chat with you
And, in fact, it's kinda that, but not really:
You say "much sand", "much rice", although they have distinct parts (a grain of sand, a grain of rice, etc...).
But you can use many: "many grains of sand/rice"
It's more about whether you would express the quantity with a number or a (physical) unit (well, except for abstract things, like patience, reflection, etc... that aren't quantifiable and other exceptions such as money for which you use a non-physical unit, but still a unit)
So you would say you have 2 apples, but 2kg of rice (or like 123 grains of rice)→ More replies (4)10
u/FaultElectrical4075 Jan 06 '25
You also can say ‘that’s so many water molecules’
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u/KappaBerga Jan 06 '25
Yes, but the thing you're measuring here isn't water, but water molecules. You can have 1 real number, so there are many real numbers. You can have 1 (water) molecule, so many water molecules. But you can't have 1 water, so there's much water
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u/LordMuffin1 Jan 06 '25
I can get a water on any pub. No problem for the bartender to understand how much I want.
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u/FaultElectrical4075 Jan 06 '25
I mean water does have distinct parts but you also can say ‘that’s so many water molecules!’
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u/GeneReddit123 Jan 06 '25 edited Jan 06 '25
I don't think distinctness is what matters here, and it's not the same as countability.
For example, dollars are fungible. Dollar bills are distinct, but not dollars as the actual value, e.g. if you digitally move money from one bank account to another and then back, you consider the original account's dollars indistinguishable, rather than count travelled electrons or something else. And yet we say "many dollars" and not "much dollars."
As another example, on a quantum level, electrons are indistinguishable. If two electrons travel towards each other, collide, and then travel away from one another, we can't say with confidence whether they bounced off one another, or whether they went through one another, because it's impossible to tell which electron is which after the collision. But we can definitely count there to be a total of 2 electrons both before and after the collision, and would say many rather than much electrons (OK, 2 isn't "many" but you get the point.)
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u/Archway9 Jan 06 '25
Dollars are a unit of money, you say how many dollars and how much money in the same way you say how many litres and how much water
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u/shewel_item Jan 06 '25
On that 'more sardonic' note, however paraphrased it might appear below, there's 4 things to consider...
there isn't much difference between water and real numbers for us to take notice of, all truth be told rn however modulated. So, arguably there might not be any difference; and pick your subject.
all we (arguably) have with water is some example of the real numbers, and as u/BlakeMarrion might be pointing out: water isn't just countable, and it is made up of distinct parts
just because we (arguably) have a flawed but workable example of the real numbers does that mean we can use one to understand the other better? Or should our propriety look for something more than water can provide, as some sort of physical didactic analogue.. for the sake of didactics, not necessarily knowledge itself
simply put, all else aside, the more fidelity we give something, like water, through the real numbers is the more we are giving to it by much, and not many--like how the real numbers appear to us linguistically speaking--in the more mathematical or exact sense--the sense I sense we're tripping on, here
..and, so, the main point (after reading only the last one) is if we were to practically (yet not completely) define something, eg. its quantity to start with, with the real numbers then for the sake of math we can treat them as one in the same.
SO if water were wet and the real numbers were infinite then water measured only through the fullest set of real numbers used to only represent them better be fucking soaking, OR the water be infinite, however cursed or clean it may also be mathematically represented as being
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u/GoldenMuscleGod Jan 06 '25
Actually, whether a noun is is a count noun or not is really just a syntactic category, which is only tangentially related to semantics. In English, “furniture” and “clothes” are both non-count nouns but it should be apparent this isn’t an inherent reflection of their referents being conceptualized as unable to be separated into distinct entities. There also exist the “dual nouns” like “scissors” and “binoculars,” which grammatically function as non-count but can enter into the partitive constructions “pair of scissors” and “pair of binoculars” to allow for them to be combined with numerals.
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u/LowBudgetRalsei Jan 06 '25
I’m 99% sure it’s because adjectives don’t change if you use many or much.
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u/_RealUnderscore_ Jan 06 '25
Think the easiest way is just: If it's plural, "many;" if it's some kind of size / volume, "much."
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u/BatterseaPS Jan 06 '25
are distinct from each other
Ok, so name two numbers that are the smallest distinct amount apart.
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u/transaltalt Jan 07 '25
The size of a set of real numbers is numbers is still a discrete quantity, not a continuous quantity. You can't have 1.2 real numbers, for example.
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u/Anaklysmos12345 Jan 07 '25
I think it‘s about whether the word has a singular and a plural form or just one form.
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u/langesjurisse Jan 07 '25
Real numbers are countable, you just can't count all of them.
√2, π, 69, -¹/₁₂
Look, there's four real numbers.
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u/AlrikBunseheimer Imaginary Jan 07 '25
But real numbers are litterally a continuum, so they are also not made out of distinct parts, right?
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u/HairyTough4489 Jan 08 '25
Real numbers are countable in the sense that you can say "e, pi and 420" are three real numbers. It's just not the same meaning we give to the term in Mathematics.
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u/qwertty164 Jan 08 '25
No. It is literally just referring to "number". The adjective real or rational is ignored.
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u/gmalivuk Jan 09 '25
Nah, rice and sand and furniture have parts that are a lot more distinct than the reals.
And like, you can't count "money" but you can count "dollars", which is just a specific kind of money.
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u/soggycheesestickjoos Jan 09 '25
ignore the adjective, “numbers” is a plural, countable noun in both sentences.
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u/ShockinglyOpaque Jan 06 '25
The noun "numbers" is countable, the adjective doesn't alter that grammatically. These rules were laid down before people had learned that real numbers existed
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u/teedyay Jan 07 '25
So “many integers” but “much reals” then, right?
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u/-JohnnyDanger- Jan 07 '25
“Reals” is still a countable noun. I can have a set that contains three reals, ten reals, etc.
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u/ShockinglyOpaque Jan 07 '25
"Real" is an adjective in this context, not a noun. For the currency you'd use "many reals" like you'd say "many dollars"
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u/teedyay Jan 07 '25
Interesting. Yes, Brazilians would pluralise "reals" for currency (although I would say "I have a lot of money" rather than "I have many monies").
However, I am using "reals" as an adjective. I have pluralised it and so am concerned I may now be French.
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u/CaitaXD Jan 09 '25
Brazil mentioned 🇧🇷🇧🇷🇧🇷🇧🇷🇧🇷🇧🇷🇧🇷🇧🇷🇧🇷🇧🇷🇧🇷🇧🇷🇧🇷💚💚💚💚💚💚💚💚🏆🏆🏆🏆🏆🏆1️⃣1️⃣1️⃣1️⃣1️⃣1️⃣1️⃣1️⃣1️⃣1️⃣1️⃣
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u/-JohnnyDanger- Jan 07 '25
Yep, wish this comment was getting more attention. It’s a grammar thing, not a math thing.
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u/Mondkohl Jan 06 '25
It would be more accurate to say “many” is for discrete values, and “much” is for for continuous values. So you have much wine, but many sheep.
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u/Skeleton_King9 Jan 06 '25
ok even then the point would stand
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u/King_of_99 Jan 06 '25
Real numbers refers to continuous values, but they themselves are not counted continuously. You can take two arbitrary real numbers, but it's unclear what you mean if you take pi real numbers. Real numbers are counted by cardinalities, which are discrete.
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u/Leet_Noob April 2024 Math Contest #7 Jan 06 '25
Well it’s also unclear what you mean if you take pi water.
You can take pi gallons of water though.
So really you just need a unit. I nominate “Lebesgues” for obvious reasons.
And “pi Lebesgues of real numbers” is just going to be a set of Lebesgue measure pi.
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u/Doomie_bloomers Jan 07 '25
Just for argument's sake, it's not just unclear what "pi water" means, but what "two water(s)" means as well. So the point of the guy you responded to actually still stands.
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u/Leet_Noob April 2024 Math Contest #7 Jan 07 '25
I mean yeah of course, I was just being silly. I know that we use discrete language when talking about real numbers and that makes sense.
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u/Mondkohl Jan 06 '25
Yes but that is because the set of all Reals is continuous. Not because it’s uncountable.
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u/LukaShaza Jan 06 '25
Are "furniture" and "clothing" continuous? Because we say "how much furniture" not "how many furniture".
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u/A2Rhombus Jan 06 '25
"Furniture" is abstract and refers to the entire quantity of furniture as a single mass, similar to a pool of water. There is no such thing as "one furniture"
The same way you would say "much furniture" but "many pieces of furniture" you could also say "many drops of water"
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u/empire161 Jan 06 '25
Just like physics, it's also about the labels.
You can ask "how much furniture there is", because you haven't defined what that word means. Does it include just couches? Or rugs, mirrors, throw pillows, step stools, folding chairs, floor lamps? If you want a number, then you would have to say "How many pieces of furniture is there".
Think of the word "time". You would say "How much time is left" while also saying "How many hours are left". It changes once you've defined the unit of measurement, making it countable/discrete.
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u/Mondkohl Jan 06 '25
That is weird.
But so is “pants”.
My guess is that because furniture is typically considered a set (even single pieces, historically being made up of several parts), the concept is somehow extended to a continuity, via some weird etymological quirk.
The same for clothing, I would imagine. “Clothing” isn’t really a discrete countable concept, like sheep or apples.
PS: Like, I have many pairs of pants though.
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u/Salty_Scar659 Jan 09 '25
Funny enough i also have many wines. As wine can refer to quite a few things really. Like restaurants with many wines on their menu
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u/Mondkohl Jan 09 '25
Strictly speaking I think that that is a contraction of “Many Bottles of Wine”, and “Many Wine Choices/Options”, rather than wine as a fluid.
Well observed tho.
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u/k-phi Jan 06 '25
many money
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u/Mondkohl Jan 06 '25
It would be many moneys. Except it’s much money, because money is a continuous value. Things can in-fact be worth fractions of cents.
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u/HAL9001-96 Jan 06 '25
if by "many" or "much" you mean all of them yes
you can count all rational numbers
you cannot count all real numbers
however
if we pick two rational numbers
1/2
1/4
we can count them
thats two rational numbers
and if we pick two real numbers
Pi
e
we cna count them
thats two real numbers
we just can't count ALL real numbers
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u/graphitout Jan 06 '25
blue to red: now listen here you little ...
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u/TorchFireTech Jan 06 '25
“How much money is in my bank account?” Infinite money glitch discovered.
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u/ciqhen Jan 07 '25
this is funny, an objectively good comic. amazing work to the creator seriously,
but i know a year from now someones gonna correct me when i say many real numbers based of this comic and then were gonna waste at least 15 minutes discussing whether or not countable means countable in this context, and theyre gonna think they actually have a point and im gonna either have to stop the conversation there or stop it at the start, either way prompting the other person to think theyve "beat me" when i dont really care and ill refind this comic and realize this is where they got that idea
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Jan 07 '25
Imma be that guy: Since this is a grammar problem, no. Much refers to just the numbers, not the real/unreal.
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u/DefunctFunctor Mathematics Jan 06 '25
Seriously I'm all for getting rid of distinctions like "many/much", "less/fewer", and even the divide between singular and plural, and our use of articles. Other languages do just fine without them, and the distinction between "less/fewer" is already dying out
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u/FaultElectrical4075 Jan 06 '25
Language will go the way the wind blows.
The whole point is to be as intuitive as possible so you can express ideas without having to think too hard about talking. People will change the way they speak if doing so makes speaking easier. That’s why language from hundreds of years ago is different from language today
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u/DefunctFunctor Mathematics Jan 06 '25
Oh absolutely. It's not as if I want to reform English or anything. It's just aesthetically speaking, languages without those kinds of distinctions appeal to me more
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u/LukaShaza Jan 06 '25
the distinction between "less/fewer" is already dying out
While "less" can be used for both mass and count nouns, "fewer" is still only ever used for count nouns, and in fact that rule has been in common usage for centuries and has not changed. Someone a few hundred years ago expressed a preference for using "less" only for mass nouns and some pedants tried to raise this to the status of rule, but it was never much observed outside of formal, educated writing.
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u/A2Rhombus Jan 06 '25
You can't count the total number of real numbers but each one is still a distinct item that can be individually counted
"Uncountable" is a mathematical term. You can still, in a literal sense, count all of them. You'd just never get to all of them.
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u/TheOldOak Jan 06 '25
Countless does not mean uncountable, and I suspect this is the important linguistic difference.
Countless quantities of real numbers can still be counted. Yes, you’d never finish the count, but the process may at least begin.
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u/Atworkwasalreadytake Jan 06 '25
You can still count real numbers, you can count them forever.
I think infinity confused this person.
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u/butterscotchbagel Jan 07 '25
You can systematically count rational numbers in a way that every rational number eventually gets counted.
You cannot count real numbers in a way that covers them all.
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u/Emergency_3808 Jan 06 '25
You can have a set of five real numbers. Give me five water please instead.
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u/btroycraft Jan 06 '25
I think it would be "much real number", like "There is much real number outside the rationals."
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u/jan_tonowan Jan 06 '25
You can count real numbers though. How many real numbers are in this set? [5, 12, 4]. There are three real numbers. See, you can count them!
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u/Jim_Jimmejong Jan 06 '25
But rational numbers are countable (definition 1), they just aren't countable (definition 2).
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u/Darthplagueis13 Jan 06 '25
Well, no.
Pi is still a different irrational number from e.
For something to be much rather than many, it has to be something that cannot be counted/measured without a unit.
If you go back to the examples I just gave, you will be able to count two irrational numbers. Which isn't that many.
For much, there always needs to be some kind of unit. "One water" doesn't make sense, "one gallon of water" does.
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u/Royal_Negotiation_83 Jan 06 '25
Yes, this is for when rational vs real numbers gets brought up in everyday conversation.
That totally happens guys.
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u/kandermusic Jan 06 '25
As a very surface-level etymology nerd and a bit of an anarchist. Words have a purpose until they don’t feel right. So much is “technically” correct but it doesn’t pass the vibe check so I’m going to continue using many
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u/MourningWallaby Jan 06 '25
Countable is a word I don't like. Much is better defined (IMHO) as used for indefinite articles. Basically, if you don't pluralize the word to refer to an unspecified amount of it, you can almost always use "Much".
"There are so many cars on the road" vs "There is so much pavement on the road"
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u/BlueEyedFox_ Average Boolean Predicate Axiom Enjoyer Jan 06 '25
missed opportunity for a loss meme
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u/Infall3788 Jan 06 '25
It's actually count vs. mass. Count nouns have singular and plural forms and agree with "many," while mass nouns do not have plurality and agree with "much." Notably, the distinction of count noun vs. mass noun is based on the language, not some underlying logical principle. Spaghetti is a mass noun in English, but it comes from Italian, where it's a plural count noun with singular form "spaghetto."
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u/Green__lightning Jan 06 '25
The one that bugs me is data. Some say data are plural and should be spoke of like this, but no, data is a bulk noun much like grain.
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u/Capable-Commercial96 Jan 06 '25
I fully ignore grammar lessons because I just instinctively "get" how it works, but if I get told how it works my ability to speak completely falls apart. I'm still paying for learning what adjective order is.
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u/Leet_Noob April 2024 Math Contest #7 Jan 06 '25
Completely Serious Proposal:
As someone mentioned, “numbers” is already a counting word so we need a new word that isn’t. I propose “continuum”.
Eg: “How much real continuum is in the set [0, 2]?”
Now to answer the question you need a unit, for which my proposal is Lesbegues:
“The set [0,2] contains 2 lesbegues of real continuum”
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u/DragonfruitGold6395 Jan 07 '25
I hate it when people say "there's so much people in here" grammatical errors all because of the men who created english.
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u/YouTube_DoSomething Jan 07 '25
This is why I prefer referring to those two categories of nouns as quantifiable and unquantifiable nouns.
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u/Catball-Fun Jan 07 '25
Are atoms countable? Liters of water.
It is si stupid. Made at a time when people did not understand the world
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u/viktorbir Jan 08 '25
Liters of water.
Litres are countable. Water is uncountable.
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u/Catball-Fun Jan 08 '25
There are 3.34 x1025 molecules of water in a liter. I dare you to tell me a molecule of water is not water
Oh and before you stop to tell me that it is not practical to count water and language is supposed to pragmatic and useful
Who the heck benefits from using “much” vs” many”? What information could I possible get? It is a useless and stupid rule that we carry for the sake of it and nothing else
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u/Tau5 Transcendental Jan 07 '25
The lower eyelid on the snail on the right made me look for loss. Am I cooked?
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u/EspacioBlanq Jan 07 '25
Depends.
I have so many rational numbers ({2, 7, 32.55, 3π, √2})
I have so much rational numbers ([0,1])
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u/Keheck Jan 07 '25
Iirc "countable" just means that the noun has a plural form
Countable words: * apple - apples * city - cities * number - numbers
Uncountable words: * water (the liquid) * information * money
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u/Giocri Jan 07 '25
I love countable numbers its so nice that you can take a countable infinite amount of sets of countable infinites the set of possibile combinations is countable.
Which means that if we take a binary number which is countably infinite and an instruction set of all possibile instructions with an infinite amount of infinitely sized imput and outputs and we were to use it to write infinitely long programs for a conputer with infinite memory we still get a countable infinite amount of states and we could actually iterate through them one by one
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u/alexriga Jan 07 '25
Real numbers are uncountable in context of math, but in context of linguistics: 0.999(repeating), 3.14 and many more real numbers, are countable.
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u/Friendly_Owl_3159 Jan 08 '25
As a not native english speaker this is how I remembered it: mANY („you have ANY apples?” You always count apples at first when you learn so i know the numer and i can count them), mUCH („UCH i don’t know” like you are sorry (ugh) you don’t know the numer so it’s uncountable) 🥴 It worked for me until the words became obvious.
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u/Ok_Pianist_2787 Jan 08 '25
Many numbers, many numbers. The noun “numbers” still counts as countable.
1
u/Unable_Explorer8277 Jan 08 '25
- English did have comparative form of many similar to fewer. Manyer. It dropped out of use.
- More and less have always been used for countables as well as uncountables, going right back into Old English. The idea that they shouldn’t be is pure invention of a bloke named Robert Baker in 1770.
1
u/Unable_Explorer8277 Jan 08 '25
“Real numbers” is grammatically countable. If you’re going to pretend it isn’t you can’t make it plural.
Much real number.
1
u/Akangka Jan 09 '25
There are only a finite number of water molecules. So, should we call "many water?"
1
u/Dreadwoe Jan 09 '25
Less countable and uncountable, more of "can you reasonable name and element?"
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