It actually does exist per the ring axioms, but it distributes over addition. So 5×5 = 5×(1+1+1+1+1) = 5+5+5+5+5, but e.g. 0.5×0.5 can't be written like that because 0.5 isn't a sum of 1's (the unit).
In the algebra we use most often multiplication is actually defined as a unique operation separate from addition. So, technically, multiplication is alongside addition and both of them "exist more" than subtraction and division (it would be more correct to say that subtraction simply derives from addition; same how division derives from multiplication). If anyone is interested, look up abstract algebra.
Is there a reason addition and multiplication are the "real" ones? Is it just that they're more intuitive? Like, would a math system built on "addition is just subtracting a negative number, and multiplication is just division by the inverse" work the same way?
I'll explain a bit of the background of this topic first.
One of the common algebras we use is a field . Because it's a field, the + and • operations within the real numbers have to follow a set amount of axioms. Some of these axioms define the existence and interactions of inverse elements, which effectively fill the roles of subtraction and division, so we don't have to make an algebraic structure (it won't be a field anymore) like this .
Your last question is essentially asking whether is a field. In this algebraic structure subtraction and division are the main operations and addition and multiplication are derived from them. If this structure is a field, it's going to work just as well as does. So, we have to check the field axioms and whether they work. Sadly, your structure fails both commutativity axioms (probably even others as well): for any elements a, b which are of R, it must hold that a-b=b-a and a÷b=b÷a. This is obviously not true for most values of a and b, therefore it's not a field. You could still use the structure and have it follow some list of axioms to make it work the same, however, it would be quite a non-standart way of approaching the problem and not worth the hassle.
It's actually very easy to define in a way that will not incur much hassle. You just enforce the axioms on the inverses (now + and \cdot). Of course this structure means absolutely nothing new and is just renaming things.
I like how people here are just like "duh that's obvious" when the point is not that division is inverse to multiplication, but that division literally does not exist but is just used as shorthand to write multiplication with the dividends multiplicative inverse. I.e. 5/4 is really 5×(4^-1) where 4^-1 is defined as the number which multiplied by 4 equals 1.
There is actually a reasonable mathematical philosophy theory that discusses whether maths actually exists or if we just made it up. We don't know for sure yet.
Mathematics is definitely a human invention. This is already clear to everyone who knows what an axiom is, but of course philosophers need to make everything more complicated than it is.
Negative numbers don't exist. You can't have -100 apples. They are abstractions to show something being removed. Multiplication and Division also do not exist. They are representations of addition.
As a female math professor I know what I'm talking about.
You can't have 4+3i apples, either. Do non-real numbers exist?
They are abstractions to show something being removed.
You could say that all numbers are abstractions for something. Positive numbers are abstractions for something being added. Do they exist? What about other abstractions? Do sets exist? Do functions exist? Is it helpful to think about a mathematical concept, which was obviously invented by humans, as existing or not existing?
Multiplication and Division also do not exist. They are representations of addition.
Why does that mean they don't exist? What if I define subtraction to exist and addition to be subtraction by the number with its sign inverted?
As a female math professor I know what I'm talking about.
Lol you don't, also why specifically point out that you're female? The question here boils down to what a number actually is. At the naive level of counting physical objects or within Peano arithmetic, you might be correct. But when seeing numbers as elements of certain rings, or fields even, negative numbers (well, additive inverses at least) and multiplication are both simply defined per the ring axioms and exist just as much as the unit element and addition.
I think you've misunderstood, they said they were a professor in "female math," not that they are female (which might also be true, but not particularly relevant).
You can learn more about "girl math" sometimes called "female math" on wikipedia: https://en.wikipedia.org/wiki/Girl_math
Ok, I can understand that in computer logic you have to define subtraction and division as "different addition" and "different multiplication", but the idea that subtraction and division don't exist is pure horseshit. If there are three apples on a table and I take one, I have subtracted an apple, not added negative one apple. I haven't taken a fucking ghost apple and put it on the table to destroy the first apple. I grabbed something positive and took it away.
Similarly if I then slice the apple I took in half, I didn't multiply it by .5, I took a whole thing and made it 2 halves. I divided it into parts.
I'm not saying that "I added negative one apple" isn't valid - as you said, sometimes fees exist. But negative numbers do not mean that subtraction and division are not equally valid concepts, because mathematics does not exist in a vacuum of context
Well not exactly. Computers use discrete number representations which means that the algorithms in hardware for multiplying and dividing are different.
yea because the structure is fundamentally a Group, both of the operations have the associative property, it has a neutral element and a unit and for every element of the Z set it exist its inverse in respect of the • operation.
thegrodyknudclump@reddit
I always knew math was gay as hell
Louner_@reddit
multiplication also doesnt exist! 5×5 is actually 5+5+5+5+5
Tokipudi@reddit
Numbers other than
1
and0
actually don't exist either!9
is just1+1+1+1+1+1+1+1+1
!Matt_2504@reddit
0 doesn’t exist either, it’s just 1 +(-1)
TinySchwartz@reddit
It's just addition all the way down
Number_Haver31@reddit
Addition doesn't exist, it's just the iterated successor function
Uncle480@reddit
Numbers don't even exist!
5 is just 🤚 = ☝️+☝️+☝️+🖕+☝️
SlovenianTherapist@reddit
So you had 1 + (-1) bitches?
UltraMadPlayer@reddit
I'd say 1 doesn't exist. 1 is just succ(0)
AnxietyResponsible34@reddit
what about 0.1
OneSushi@reddit
oh yeah? Define multiplication in terms of addition for 5 * pi.
Part 2:
Define exponentiation in terms of multiplication for an irrational exponent (5^ pi)
Part 3:
Define trigonometric functions… period?
(Note: you’ll have to use lots of proof based calculus)
(Reference sheet: Michael Spivak’s ‘Calculus’)
Gositi@reddit
It actually does exist per the ring axioms, but it distributes over addition. So 5×5 = 5×(1+1+1+1+1) = 5+5+5+5+5, but e.g. 0.5×0.5 can't be written like that because 0.5 isn't a sum of 1's (the unit).
CompisPaDum@reddit
("ummm, akschuallly..." moment incoming)
In the algebra we use most often multiplication is actually defined as a unique operation separate from addition. So, technically, multiplication is alongside addition and both of them "exist more" than subtraction and division (it would be more correct to say that subtraction simply derives from addition; same how division derives from multiplication). If anyone is interested, look up abstract algebra.
Cerxi@reddit
Is there a reason addition and multiplication are the "real" ones? Is it just that they're more intuitive? Like, would a math system built on "addition is just subtracting a negative number, and multiplication is just division by the inverse" work the same way?
CompisPaDum@reddit
I'll explain a bit of the background of this topic first.
One of the common algebras we use is a field. Because it's a field, the + and • operations within the real numbers have to follow a set amount of axioms. Some of these axioms define the existence and interactions of inverse elements, which effectively fill the roles of subtraction and division, so we don't have to make an algebraic structure (it won't be a field anymore) like this .
Your last question is essentially asking whether is a field. In this algebraic structure subtraction and division are the main operations and addition and multiplication are derived from them. If this structure is a field, it's going to work just as well as does. So, we have to check the field axioms and whether they work. Sadly, your structure fails both commutativity axioms (probably even others as well): for any elements a, b which are of R, it must hold that a-b=b-a and a÷b=b÷a. This is obviously not true for most values of a and b, therefore it's not a field. You could still use the structure and have it follow some list of axioms to make it work the same, however, it would be quite a non-standart way of approaching the problem and not worth the hassle.
DarkSkyKnight@reddit
It's actually very easy to define in a way that will not incur much hassle. You just enforce the axioms on the inverses (now + and \cdot). Of course this structure means absolutely nothing new and is just renaming things.
Idiot_of_Babel@reddit
Just add [3,2] to itself [-7,3] times
StarvinPig@reddit
But in set theory multiplication is defined via addition (Which is in turn defined by successor function)
Arstanishe@reddit
yeah, because you then can multiply other stuff. vectors, matrices, etc
Exxeleration@reddit
Teto alert‼️‼️
AntiProtonBoy@reddit
Additions don't exits either, they are just xor operations.
Acronym_0@reddit
Squares dont exist!
5² is just 5x5, ie 5+5+5+5+5
Gositi@reddit
I like how people here are just like "duh that's obvious" when the point is not that division is inverse to multiplication, but that division literally does not exist but is just used as shorthand to write multiplication with the dividends multiplicative inverse. I.e. 5/4 is really 5×(4^-1) where 4^-1 is defined as the number which multiplied by 4 equals 1.
whydoyouevenreadthis@reddit
When you say "division doesn't exist", what do you mean by that? Does multiplication exist? Can you prove it?
lessself2b@reddit
whydoyouevenreadthis@reddit
Negative numbers do not require subtraction. (Subtraction is a binary operator, while the - in -1 is a unary operator.)
IamWatchingAoT@reddit
There is actually a reasonable mathematical philosophy theory that discusses whether maths actually exists or if we just made it up. We don't know for sure yet.
whydoyouevenreadthis@reddit
Mathematics is definitely a human invention. This is already clear to everyone who knows what an axiom is, but of course philosophers need to make everything more complicated than it is.
DreamDeckUp@reddit
My opinion is that math is language that we use to describe a fundamental truth about the world. Whether that language is correct is another question.
ModmanX@reddit
Division and subtraction are opposites of addition and multiplication.
Aka shit I was taught as an 8 year old. Only in 4chin would this be seen as a big revelation
NanoYohaneTSU@reddit
Negative numbers don't exist. You can't have -100 apples. They are abstractions to show something being removed. Multiplication and Division also do not exist. They are representations of addition.
As a female math professor I know what I'm talking about.
whydoyouevenreadthis@reddit
Do positive numbers exist?
You can't have 4+3i apples, either. Do non-real numbers exist?
You could say that all numbers are abstractions for something. Positive numbers are abstractions for something being added. Do they exist? What about other abstractions? Do sets exist? Do functions exist? Is it helpful to think about a mathematical concept, which was obviously invented by humans, as existing or not existing?
Why does that mean they don't exist? What if I define subtraction to exist and addition to be subtraction by the number with its sign inverted?
Gositi@reddit
Lol you don't, also why specifically point out that you're female? The question here boils down to what a number actually is. At the naive level of counting physical objects or within Peano arithmetic, you might be correct. But when seeing numbers as elements of certain rings, or fields even, negative numbers (well, additive inverses at least) and multiplication are both simply defined per the ring axioms and exist just as much as the unit element and addition.
Munnin41@reddit
Why does being female matter here?
afwaller@reddit
I think you've misunderstood, they said they were a professor in "female math," not that they are female (which might also be true, but not particularly relevant).
You can learn more about "girl math" sometimes called "female math" on wikipedia: https://en.wikipedia.org/wiki/Girl_math
Munnin41@reddit
Oh that makes more sense
MonasteryFlock@reddit
That’s what I’ll tell the bank if I ever overdraft my account. “What do you mean? Negative numbers don’t exist!”
Mylxen@reddit
Of course you can have -100. When you are in debt.
Spiritual_Bus1125@reddit
"are opposite" imply that they exist as a concept, that OP is saying is thst they do not
For a place where it matter, computers. Weird math wizzardy.
whynotlaptop@reddit
Ok, I can understand that in computer logic you have to define subtraction and division as "different addition" and "different multiplication", but the idea that subtraction and division don't exist is pure horseshit. If there are three apples on a table and I take one, I have subtracted an apple, not added negative one apple. I haven't taken a fucking ghost apple and put it on the table to destroy the first apple. I grabbed something positive and took it away.
Similarly if I then slice the apple I took in half, I didn't multiply it by .5, I took a whole thing and made it 2 halves. I divided it into parts.
Spiritual_Bus1125@reddit
You are using your intuition, it is not that simple when talking about math.
While it's strange to think about "I added negative 1 apple" is a perfectly reasonable way to think about the subject.
whynotlaptop@reddit
I'm not saying that "I added negative one apple" isn't valid - as you said, sometimes fees exist. But negative numbers do not mean that subtraction and division are not equally valid concepts, because mathematics does not exist in a vacuum of context
Stuffssss@reddit
Well not exactly. Computers use discrete number representations which means that the algorithms in hardware for multiplying and dividing are different.
Spiritual_Bus1125@reddit
...depends but mostly no.
Only specialized computers have hardware dedicated to division.
It's all multiplication bby
Automatic_Humor_8167@reddit
they say politics is hollywood for ugly people
math is art for virgins
moidcrush@reddit (OP)
he gets his insides rearranged each night desu
SpaceBug176@reddit
How do you know
GodOfMegaDeath@reddit
OP does the TOPPING
SpaceBug176@reddit
Yeah nah, someone that uses "desu" at the end of their sentences is not getting laid.
moidcrush@reddit (OP)
makes two of us then spacebug
SpaceBug176@reddit
I said at the end of their sentences.
fritando@reddit
no but really, I'm a math major and sometimes when i have sex my mind wanders to mathematical concepts like that
moidcrush@reddit (OP)
psycho
kahenkilohauki@reddit
Is this the same guy that got hate fucked so hard by his boyfriend due to similar mathematical notations?
Mayo_Kupo@reddit
If you call yourself a "math bottom," you're full of crap.
The term is denominator.
jwji@reddit
Next he'll have the revelation that harder substances scratch softer substances.
infinitegestation@reddit
As a bottom he may already have had that particular revelation
SpaceBug176@reddit
Well duh, that was literally the joke.
Geilomat-3000@reddit
Am bottom and mathematician, can confirm
b0b89@reddit
Addition doesn't exist it's actually the inverse of subtraction
dylan_klebold420@reddit
what an autistic way to write 0.25
DreamDeckUp@reddit
it's meant to highlight the fact that 0.25 is the multiplicative inverse of 4 because 4 × 0.25 =1
StarvinPig@reddit
That's 1.25
dylan_klebold420@reddit
i meant the 4^(-1) specifically, should've been clearer
LilMissBarbie@reddit
A math bottom?
And it has divisions?
Who's the top in a math division?
The smartest nerd?
DreamDeckUp@reddit
they call him the numerator
StarvinPig@reddit
Topologists
CrazyJellyGuy1@reddit
Topologists is so good lmao
MrShoe321@reddit
Everytime
sadPonderosaEnjoyer@reddit
yea because the structure is fundamentally a Group, both of the operations have the associative property, it has a neutral element and a unit and for every element of the Z set it exist its inverse in respect of the • operation.
8123619744@reddit
Can’t divide by 0
sadPonderosaEnjoyer@reddit
sorry I chose the wrong set, the correct one is
railxp@reddit
You're not fucking them, they're fucking you with their ass
Quantum_Sushi@reddit
Bottom mathematicians are a more widespread thing than we'd think
moidcrush@reddit (OP)
its the same boy
NanoYohaneTSU@reddit
Thank god I'm not a bottom.
FireDevil11@reddit
Is this the same math bottom from that other greentext where he pisses off his top bottom by making stupid math statements so he anger fucks him?
moidcrush@reddit (OP)
Yes same bottom
Adrian4lyf@reddit
So if bottoms are good at math, what are tops good at?
moidcrush@reddit (OP)
putting their dick in bottoms
Adrian4lyf@reddit
Prawnyman@reddit
Oh sweet, it's this guy again https://www.reddit.com/r/greentext/comments/ql56f4/anon_is_a_bottom_mathematician/
Dd_8630@reddit
That maths bottom is on the middle of that meme with the Gaussian curve.
Dabox720@reddit
Dang thats crazy. I figured that out when they got introduced in elementary school.
NoTmE435@reddit
« And then he came »
flochu69@reddit
Not a Greentext
harveyshinanigan@reddit
why is manly on this post ?
AustralianSilly@reddit
“Math is for virgins”