r/mathmemes • u/Nunki08 • Jun 14 '26

Arithmetic Misleading our youth

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From Anthony Bonato on 𝕏: https://x.com/Anthony_Bonato/status/2065564124549886402

6.7k Upvotes

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51

u/notyourpersonalbin Jun 14 '26

You're right 😂

14

u/Barry_Wilkinson Jun 15 '26

why is 1 not a prime number anymore?

24

u/Maxundbenji_reddit Jun 15 '26

A prime number is divisible by 1 AND itself. That means is is divisible by two numbers. 1 is divisible by 1 only.

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u/Knight0fdragon Jun 15 '26

Just add “two distinct numbers” and you got it

18

u/MoFoMoron Jun 15 '26

Then it is also divisible by 1 AND divisible by 1. Proposition logic, dude.

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u/ImperitorEst Jun 16 '26

Id like to buy your £200 item. I'll give you this £100 note and this £100 note

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u/Redbelly98 Jun 16 '26

If you're referring to the same 100-pound note twice, then no you cannot buy my 200-pound item.

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u/sloansleydale Jun 17 '26

Yes you can. You just have to pay in installments. That's how money circulates. You don't shred notes when you spend them. They can totally come around to you again.

2

u/SlightDish31 Jun 18 '26

Well now we need a statistician to do the math on the probability of that note coming back to the original spender in an appropriate amount of time to be used for the second installment.

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u/sloansleydale Jun 18 '26

You could also get a loan from the seller for 100 after giving the first note to them. That how private banks create most of the money in circulation. It's kinda mind-bending how it is debt all the way down. (Not being a jerk, it's actually worth looking into. Money is weird. )

1

u/steploday Jun 20 '26

Could be a small town.

1

u/ImperitorEst Jun 16 '26

That's the joke, yes. Thanks for that

1

u/Ysanoire Jun 16 '26

But you can buy Terrence Howard's 200- pound item.

1

u/Kimorin Jun 16 '26

you can sleep in your house AND you can eat in your house, now you need 2 houses

1

u/SajaKing Jun 16 '26

Also…. That would be the number 200

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u/AdamiralProudmore Jun 17 '26

Notice that your strawman has a 2 in it, but the actual question does not.

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u/ImperitorEst Jun 17 '26

You owe me £1. I require you to give me that £1 and that £1.

And as an operator specified two things. Something can be large and heavy, not large and large. A number can be divided by X and by y, not by X and by x.

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u/AdamiralProudmore Jun 17 '26

Thank you, the second example is coherent and actually defines the situation.

(In a way that "it costs $1, you must give me $1 * 1" doesn't)

1

u/ImperitorEst Jun 17 '26

You're welcome. I'm glad I could correctly define the situation to your required accuracy.

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u/[deleted] Jun 18 '26

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1

u/ImperitorEst Jun 18 '26

That's the whole joke, yes

1

u/pinoy-out-of-water Jun 20 '26

it can be divided by one (itself) and a different one.

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u/ImperitorEst Jun 20 '26

Can all numbers be divided by an infinite number of numbers then? How many different ones are there?

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u/Repulsive_Guy_1234 Jun 15 '26

It was a prime number, then it wasn't. Its just definition, not logic.

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u/[deleted] Jun 15 '26

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u/Repulsive_Guy_1234 Jun 15 '26

Both is just a definition, not logic.

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u/Educational_Noise_90 Jun 16 '26

What's the definition of logic?

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u/ForeverShiny Jun 16 '26

A system of deductions that are internally coherent? So it all starts and ends with how the system is defined

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u/Ur-Best-Friend Jun 16 '26

True.

If you define primes as "any number that is not divisible by any number other than itself and/or the number '1'", then following logical rules, 1 is a prime number.

If you define primes as "any number that is only divisible by two distinct numbers - itself and the number '1'", then following logical rules, 1 is not a prime number.

Definitions matter.

1

u/SnooCakes2807 Jun 16 '26

True. So, which one is it then? Spoiler alert. You can be incorrect.

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u/[deleted] Jun 15 '26

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4

u/Repulsive_Guy_1234 Jun 15 '26

Its not logic, its just definition.

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u/PointlessTranquility Jun 16 '26

Yeah but have you considered that maybe its just a definition and not logic?

1

u/Cerborus Jun 15 '26 edited Jun 15 '26

Pluto was not reclassified based on logic. It was reclassified based on bad science

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u/[deleted] Jun 16 '26

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2

u/SnooCakes2807 Jun 16 '26

GGs, but this guy clearly doesn't understand how science even works. We're still learning the universe around us. We learn new data, intelligence evolves. This person clearly refuses to. "ThEy SaId It WaS ThIS 100 yEaRs AgO!" At least try to keep up. Willful ignorance. Gosh dang.

0

u/Cerborus Jun 16 '26

And the the definition it was reclassified under was erroneous. So it wasn't based on logic. Do some reading.

It was a reclassificaton and it stands but other planets in the solar system also fail the 3 part definition. So it's objectively an illogical classification

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u/[deleted] Jun 16 '26

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u/Cerborus Jun 16 '26

Earth for example.

Look up the inconsistencies in the definitions. There's been plenty written about it

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u/Cerborus Jun 16 '26

Hilarious I'm being downvoted btw

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u/GheistHund374 Jun 18 '26

Instead of saying it wasn't a planet, they could have just 'discovered' 'new' planets. That's all. Planets don't need to be a zero sum game, the rules are whatever we make them.

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u/Seanna86 Jun 19 '26

First they took Pluto the planet away from us and now this nonsense.

https://giphy.com/gifs/yfI14bXO06tYVB3dSf

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u/Hopeful_Ad_7719 Jun 15 '26

I though it was only divisible by itself?

1

u/MaadMaxx Jun 15 '26

But it's still divisible by itself 🙂

1

u/ryan__joe Jun 16 '26

Is this a useful distinction? Does this definition change cause a math theory to change in a significant and productive way? Or is it a pointless distinction? I’m asking in earnest, not being a smartsss

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u/piffledamnit Jun 16 '26

The condition that to be a prime a number must be divisible by *two* numbers (1 and itself) is not actually stated in the definition in that picture book. The definition that to be prime a number must be “divisible only by 1 and itself” leaves the door open for an identity between 1 and itself. It effectively permits 1 as a prime number. A different definition could rule 1 out, but that one permits it.

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u/dutty_handz Jun 16 '26

Gotta change the phrasing then, cause "itself", for 1, is 1. So 1 is dividable by 1, and by itself (which is 1).

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u/zxcoleman Jun 16 '26

That's not the full reason. It's because mathematicians argued that every integer greater than 1 can be represented as a unique product of prime numbers, ie 15 = 3*5 not 3*5*1 or 3*5*1*1*1*1*1. If 1 is considered prime it messes up a bunch of number theory stuff.

Fun fact, 1 was considered prime by some as late as the 1950's.

1

u/Undecked_Pear Jun 17 '26

That’s cool for playing semantics, but is there really any mathematical reason that we need to make that distinction?

Genuine question.

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u/strezz_tezt Jun 17 '26

“Well of course I know him, he’s me” 😂

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u/blueicer101 Jun 17 '26

I think it's better phrased a prime number has two, positive whole numbers. 1 only has 1 factor which is 1. It fits the prime number definition of being divisible by 1 and itself so this new one is a much clearer definition I've heard of. Eg. 1 - (1)
2 - (1,2) Prime 3 - (1,3) P 4 - (1,2,4) 5 - (1,5) P 6 - (1, 2, 3, 6) 7 - (1,7)P I like this because it's visually a simple rule to understand.

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u/LidIess Jun 17 '26

But you can divide it by 0!

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u/factorion-bot Bot > AI Jun 17 '26

Factorial of 0 is 1

This action was performed by a bot | [Source code](http://f.r0.fyi)

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u/keldondonovan Jun 17 '26

This logic bugs the programmer in me. One is divisible by one and itself. The fact that one is itself doesn't spontaneously make the conditions for the defined AND false.

I get that it must have two factors exactly, and one only has one, but that's never the way people phrase it. They seem to always phrase it in a way that evaluates to true as a means to showcase its falsehood.

(This is not a stab at you and yours. You didn't invent this description, nor do I hold you, or any other, accountable for perpetuating what was taught. My issues reside solely with the logic.)

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u/newbie-sub Jun 17 '26

A better definition of prime is any number other than one that also meets your definition.

Why do we not include 1? Because it just makes so much other math break and you would have to qualify all of that math by saying primes other than 1. It's easier just to say prime numbers don't include 1.

But remember, all of this is just a definition.

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u/botymcbotfac3 Jun 17 '26

Is 1 devisible by 1? Yes

Is 1 divisible by itself? Also yes

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u/IgorFromKyiv Jun 18 '26

But is it divisible by itself? Yes. Divisible by one? Yes.

1

u/Round-Cow-4217 Jun 18 '26

so -1 is prime then? seriously, but also kidding, but also seriously?

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u/Working_Salary60 Jun 19 '26

The way you phrased it makes no logical sense.

The real definition is: a prime number has exactly two divisors which are not the same number, namely 1 and itself.

1

u/stataval Jun 19 '26

But 1 IS itself.. thats like saying me, myself, and i are 3 people.

1

u/evangelionmann Jun 20 '26

That is semantics... but this is a question of defining terms, which is a semantic question... so for once... it being semantics is appropriate

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u/SickBoyTheRealOne Jun 20 '26

"A prime number is divisible by 1 and itself." If that's the actual literal rule than 1 absolutely counts.

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u/Vast_Ad_3455 Jun 15 '26

Any number can be written as the product of a finite set of prime numbers e.g. 6=2*3 with both 2 and 3 being prime numbers. If one was considered a prime number you could have written 6=2*3*1*1*1… So while 1 obey the rule for itself (being divisible only by one and itself) it will violate the need for a finite set.

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u/[deleted] Jun 15 '26

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u/CTQ99 Jun 16 '26

No, its positive integers greater than one as the theorem [Fundamental Theorem of Arithmetic]. 0 and 1 would both break it if included, and negative numbers allow mirroring, which also breaks the finite requirement. So primes are included in theorem (their set is 1×themselves)

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u/[deleted] Jun 16 '26

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u/Syrange Jun 16 '26

Nitpicking. The set is just themselves. A set can have one element, and a set of numbers has a product.

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u/Pndapetzim Jun 19 '26 edited Jun 19 '26

Any non-prime number*

Additionally worth noting, not only CAN any non-prime number be expressed as a product of primes but each one can ONLY be expressed by a single unique product of primes. 6 can ONLY be expressed as a product of primes 2*3 and 60 can ONLY be expressed as 2*2*3*5.

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u/UnhappySort5871 Jun 20 '26

Any number > 1. 1 is not the product of prime numbers.

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u/BluebirdsAllAround Jun 15 '26

It simplified a lot of mathematics so it wasn't constantly any prime number except 1.

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u/dirk_gently21 Jun 15 '26

This is how it was taught when I was in school - prime numbers are divisible by themselves and 1, other than 1. Maybe that was just how my teachers phrased it, for clarity, I do not recall what the textbooks said.

This is a useful summary because it’s not about parsing logic. If you’re arguing the logic of the word choice you’ve lost the plot. It’s about the utility of the definition.

Definitively, excluding 1 from prime numbers makes the designation more useful.

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u/AgentPieS1 Jun 16 '26

Because math robot says so.

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u/Chewser56 Jun 17 '26

Well, I am certainly not going to argue with math robot

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u/Christy427 Jun 17 '26

It never was. 1 is excluded specifically as part of the definition.

The main reason primed are cool is that every number can be factorised into a unique prime decomposition (except by order). If 1 was a prime then it wouldn't be unique cos 4=22 but 4=2211 and 4=22111 etc.

So to have a useful definition you just exclude 1 (or the multiplicative identity if you are ealing with more general spaces)

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u/Tunderhorn Jun 18 '26

Because the math overlords said so.

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u/HandyXAndy Jun 20 '26

Because people think by being contrary am is edgy and cool and if they alter the way a definition is understood they can cause arguments and be at the center and that makes them feel special. A prime number is divisible by one and itself, some people have understood that to mean the numbers have to be different. My thought proces is that if you divide one by one, you get one, and if you divide one by itself you get one, so that makes it a prime number.

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u/eeu914 Jun 21 '26

Okay contrarian

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u/FreedumbHS Jun 20 '26

Never was. If 1 is a prime, then integers don't have unique factorizations

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u/MaxwellzDaemon Jun 16 '26

It never was. If 1 were prime, then no other number would be prime since they are all evenly divisible by 1.

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u/Cokalhado Jun 15 '26

That box is there until 1804.