Multplication and Division

[Anonymous No.14823545]

Not a troll question. This is a deep topic that only looks simple at a first glance. But, what is division, actually?

Multiplication is often taught as repeated addition. This makes sense, no qualms here. But then division is often taught as the opposite of multiplication: repeated subtraction. This is a bad analogy, isn't it? In some ways, it's like subtraction. But what about when you have remainders? Or quotients with repeating decimals? It kind of stops making sense at that point. It's like there's something extra to division, don't you think?

What's going on here? You can go online and see forums of primary school teachers who hate "New Math" because they're being forced to teach simple stuff in unintuitive, confusing ways.

[Anonymous No.14823557]

>>14823545
>what is division, actually?
Multiplication with the inverse element to a number. The inverse element is the element that bringt a number to 1. You can represent it as [math]a^{-1}[/math] or say that you "divide by a". What do you need to multiply 5 with to get 1? [math]5^{-1}[/math]

[Anonymous No.14823564]

>>14823545
>multiplication is simple
wait until you multiply two numbers together that both less than 1

[Anonymous No.14823570]

>>14823557
Then what is multiplication? Why can you multiply by zero but not divide by zero? Why is multiplication always "clean" but division sometimes isn't (e.g. requires remainders)?

[Gwaihir No.14823576]

Division is derivation. Of equal portionality, where prior to the calculation the exactitude of that portionality is unknown but the totality is.

When multiplying digits below a value of 1 you are technically dividing, reciprocally

Multiplication is amassing of equal portionality where prior to the calculation the portionality is known, but the totality is not.

[Gwaihir No.14823577]

>>14823570
You CAN divide by zero. It returns an output that is "infinity" x the numerator.

[Anonymous No.14823580]

>>14823576
Silly question, but humor me here. Which do you prefer, multiplication or division? Why?

[Anonymous No.14823581]

>>14823570
>Why is multiplication always "clean" but division sometimes isn't (e.g. requires remainders)?
What's clean? For every element in a multiplication, there's an element that cleanly brings it to 1. Remainders are just a feature of representation in base 10, nothing fundamental.

[Anonymous No.14823582]

>>14823576
>>14823577
OP, ignore Gwaihir, he's a literal schizophrenic.

[Anonymous No.14823586]

>>14823581
>Remainders are just a feature of representation in base 10
I heard that Lagrange tried to get Revolutionary France to adopt a base 11 number system, so that measurements would always be clean, and fractions would be easy to compare with each other (e.g., no worrying about whether 4/7 or 7/13 was larger than another). How exactly would that work? What's the downside of using base 11?

The French Revolutionaries also considered using base 12 because it's even easier to divide in base 12 compared to base 10. And that the Maori supposedly counted in base 11, though idk how that would work.

[Anonymous No.14823589]

>>14823582
Nah, I think I'll ask him questions. He sees things most people don't, so he's interesting to me. I trust myself to filter what make sense from what doesn't.

[Gwaihir No.14823653]

>>14823589
Thank you sir.

My brothers and I decided the fairest way to share something we needed to split three ways; the person who divides the thing to be split, gets last pick.

[Anonymous No.14823743]

>>14823653
>My brothers and I decided the fairest way to share something we needed to split three ways; the person who divides the thing to be split, gets last pick.
Before I ask questions, what is the structure of the metaphor? By deciding "the thing", you mean before you choose any thing for everybody to share? Or do you only mean something like Rawls's veil of ignorance, where he argues that one ought to consider what would happen if they were placed at the very bottom before implementing social change.

[Gwaihir No.14823801]

>>14823743
It means if you cannot properly divide and share, you deserve to get the smallest share.

Anyone who would seek to make themselves both the divider and the chooser is a dishonest theif who intends to use the position to cheat you.

This is also why communism never works.

By failing to keep language axiomatically defined, you empower the totalitarian tyrant to both define and pick their portionality.ive provided you all with a comprehensive methodology for keeping language sensical. .most of you would prefer to be niggers and crack jokes though.

[Anonymous No.14823837]

>>14823801
A language that is unambiguous (like Leibniz's characteristica universalis) can easily lead to tyranny. Ambiguity allows one to escape the machinations of somebody evil. It's not a bad thing.

[Gwaihir No.14823846]

Words, conceptualizations, ideals, are not "social constructs" any nigger who tells you this is attempting to jostle these things from their objective positioning to better situate themselves to exploit the resulting dis-parity. Why do you think a Star of David (Rempan) is two triangles schismatically dislodged from it's proper position as a rhombus-like octohedron?

>Picrel

[Gwaihir No.14823855]

>>14823837
Leibinz is a Edomites kike who has a vested interest in saying such things.

[Anonymous No.14823864]

>>14823846
>Words, conceptualizations, ideals, are not "social constructs"
They are and they aren't. To make it blunt, words are living beings. Anybody who thinks they aren't, or that they should be "ossified", should take a careful look at the Tower of Babel from the Bible.
>>14823855
Saying what things? I think that Leibniz and you agree on the premise of language, or at least the idea that language can be made better if we preserve a certain snapshot of its meaning.

[Gwaihir No.14823871]

>>14823864
Language is not subjective. Math is not subjective. Physics is not subjective. I don't care what leibinz says. Don't you have your own ideas? Are you incapable of forming a thought without referencing someone else?

[Anonymous No.14823912]

>>14823871
>Language is not subjective.
How many meanings can word have, potentially?
>Math is not subjective.
Only after deciding the premise. Who chooses the premise?
>I don't care what Leibniz says.
Actually, he says what you believe. That's what I'm trying to tell you, but you keep ignoring me because you're dead set in your ways.
>Don't you have your own ideas? Are you incapable of forming a thought without referencing someone else?
Reading Leibniz and seeing his shortcomings for myself is what turned me away from him. You two have much in common, which is amusing for me because you called him an Edomite kike. I mean, look at:
https://en.wikipedia.org/wiki/Characteristica_universalis
and try to tell me that you guys disagree.
>protip: you hold virtually the same position on language, mathematics, etc. Leibniz is a hyper-Platonist and always considered himself as such.

[Gwaihir No.14823931]

>>14823912
>Actually, he says what you believe. That's what I'm trying to tell you, but you keep ignoring me because you're dead set in your ways.

Perhaps I need to give more time to consider before responding. Noted.

[Gwaihir No.14823949]

>>14823912
Understand that I quit smoking cigarettes cold turkey August 24th so I'm a little short on patience and more irritable than I normally would be, if we can even define "normally" after smoking for 25 years.

[Gwaihir No.14823984]

>>14823912
I'll leave a tab open and read about this universal language construct leibeinz discusses and dig into the source material.

https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis

This cross references with Tegmark,'s assertions btw. I emailed him (Tegmark) a couple days ago with axiomatic theory.

Thanks.

[Anonymous No.14824055]

>>14823949
No worries. No offense taken. We've spoken quite a bit over the past month. I respect what you have to say.

[Anonymous No.14824087]

>>14823984
You'll love Leibniz. He's so fascinating. He basically invented the foundations of computer science trying to parse the I Ching (binary logic). And he was the Platonist trying to dunk on Newtonian empiricism back during wars over the invention of calculus, the mechanism of gravity, etc. Leibniz's intuitions about space ended up resembling Einstein's spacetime relativity. In contrast, Newton was the absolutist, but he won out at the time.

Best of luck on quitting cigarettes. It's a grueling change for sure, but it's worth it.

[Gwaihir No.14824131]

>>14824055
You should look into the etymology of "machanayim" for some interesting reading, especially how Genesis 32 uses it in the orthodox Jewish Bible. Then, look into the schoolyard game called machanayim.

Thanks for the contextual reading source

[Gwaihir No.14824150]

>>14824087
Yeah I don't language "ossifying" as you put it, rather, it remains interlocked on crystalline matrix of meaning making reverberating between it's neighboring forms; not just shirking neighboring forms entirely as militant leftists bent on redefining the lexicon, entirely, would have us believe

[Anonymous No.14824180]

>>14824131
>machanayim
Whoa, that’s pretty cool.
>>14824150
Personally, I think that the “characteristica universalis”, if it’s real, would likely be ambiguous. It would have no direction. So you could interpret anything you wanted from it. There’s a similar problem with texts—they still retain some “direction”, but much context is lost. This is why there is a strong penchant for oral traditions over written traditions—think about the power of conversation, body language, tone, etc., that is missing from text. If one had a cipher, then you could read the text easily. But having a cipher for a philosophical text is like already having understanding before you read the text already. A “false” cipher means reading only what you want from it.

[Anonymous No.14824981]

bump

[Anonymous No.14825301]

>>14823837
>>14823801
>>14823743
>>14823653
>>14823589
>samefagging
good lord

[Anonymous No.14825396]

>>14825301
if you think they’re samefagging then you’re even more schizophrenic than the schizo

[Anonymous No.14825402]

>>14823545
>Multiplication is often taught as repeated addition
use this definition to multiply pi by e
>inb4 finitard screeching

[Anonymous No.14825410]

It is the inverse of multiplication. It goes backwards. 5*3 = 15, 15/3 subtracts 5 twice. But that implies an open field rather than inductive.

[Anonymous No.14825429]

>>14823545
>But, what is division, actually?
I could tell you

[Anonymous No.14826518]

>>14823545
why can you multiply any number by 0 and it's fine, but you divide a number by 0 and you get some weird indeterminate shit?

[Anonymous No.14827369]

>>14823557
>>14823581
>can't divide by zero

[Anonymous No.14827504]

>>14823545
>Multiplication is often taught as repeated addition
Since you said this, I am only going to talk about the integers.

The quotient of [math] x \div y [/math] is that many times you need to add [math] y[/math] to itself to form the greatest integer less than [math] x [/math], while the remainder is the amount of [math] x[/math] that is left over. So for example: [math] 20 \div 10 = 2 [/math], while the remainder of [math] 21 \div 10 [/math] is [math] 1 [/math] since 2 [math] 10 [/math] form [math] 20 [/math], so what's left over is [math] 1 [/math].

No amount of 0's can be added to itself to form a non-zero number, hence [math] x \div 0 [/math] is undefined. You may think the remainder is [math] x [/math], but it is not, since the remainder is necessarily defined to be less than the divisor. This constraint is necessary to make division have unique solutions. Any amount of [math] 0 [/math] can be added to itself to form [math] 0 [/math], hence, it has infinitely many quotients with remainder [math] 0 [/math]. However, major axioms of mathematics requires equality to be reflexive and transitive, so one thing cannot be equal to unequal things. Therefore [math] 0 \div 0 [/math] is also undefined.

Mathematically for any dividend and non-zero divisor [math] x, y [/math], the quotient and remainder [math] q, r [/math] is defined to be that pair of numbers that satisfy the equation:
[eqn] x = qy + r \qquad 0 \leq r < |y| [/eqn]
Uniqueness and existence of quotient and remainder is given by the following theorem:
[eqn] \textbf{Theorem } \text{(Division algorithm)} \left( \forall x, y \in \mathbb Z \right) \bigl[ y \neq 0 \implies \left( \exists!\; q,r \in \mathbb Z \right) \left( x = qy + r \land 0 \leq r < |y| \right) \bigr] [/eqn]

[Anonymous No.14827528]

>>14827504
>I am only going to talk about the integers.
Actually, I lied I will also talk about the Reals to make the finicucks seethe. Multiplications for the reals is much more complicated and requires a course in Real Analysis with emphasis on the construction of the Reals (preferably with cuts). Division is generally not required for the reals since the existence of multiplicative inverses act as a substitute for them: [math] \forall x \in \mathbb R \quad x \neq 0 \iff \exists x^{-1} \in \mathbb R \quad x \times x^{-1} = 1[/math], and [math] \forall x, y \in \mathbb N \quad y \neq 0 \implies \exists z \in \mathbb R \quad z = q + \left( r \times x^{-1} \right) = x \times y^{-1} [/math]

[Anonymous No.14827594]

>>14823545
The repeated addition idea only works for integers, what's 4×0.3? 4 added to itself 0.3 times?? Such ideas only go so far, when extending them to the reals your intuitive notions all fall out, e.g 3^1.232 makes no sense if you define it as 3 times itself 1.232 times.

Strictly speaking, division is defined as such: a/b=c iff a=bc for nonzero b and that's the end of the story, nothing about subtraction or anything.

[Anonymous No.14827604]

>>14827504
It should be greatest multiple of [math] y [/math] less than or equal to [math] x [/math].

[Anonymous No.14828313]

>>14827504
What happens when you begin to see division as a way of grouping? What would it mean to ask for 0 groups, e.g. 15 ÷ 0?

>>14827594
>The repeated addition idea only works for integers, what's 4×0.3? 4 added to itself 0.3 times??
You add a smaller portion of 4.
>Such ideas only go so far, when extending them to the reals your intuitive notions all fall out, e.g 3^1.232 makes no sense if you define it as 3 times itself 1.232 times.
You add 3 once and then you add a smaller portion of 3.

[Anonymous No.14828334]

>>14823545
>Multiplication is often taught as repeated addition. This makes sense, no qualms here
Then calculate e*pi by repeatedly adding.

[Anonymous No.14828341]

>>14828334
>Then calculate e
>Then calculate pi
This is where you run into problems

[Anonymous No.14828352]

>>14828341
>you run into problems
I don't run into problems because I understand that multiplication is not repeated addition.

[Anonymous No.14828865]

>>14828313
Natural division is much easier to think of when you work with them with base 1. Basically, think of the numbers as sticks. By 10 divide by 2, we mean to separate 10 sticks into 2 groups such that both group contain the same number of sticks; the number of sticks in each group is the quotient; that sticks that cannot be contained in any of the two groups is the remainder. What does it mean to separate 10 sticks into 0 groups? Nothing, exactly why it is undefined. You have to have at least 1 group of 10 sticks. What does it mean to separate 0 sticks into 0 groups? It could be anything really. If you have 0 groups of 100 sticks each, or 20 sticks each, or 0 sticks each, at the end you still have 0 sticks.

[Anonymous No.14828881]

>>14828865
I mean, if you have 0 groups of however many sticks, you essentially have 0 sticks. So separating 0 sticks in 0 groups has infinitely many solutions, since you could put as many sticks as you want in your 0 groups, while still achieving 0 sticks in the end.
Similarly, by separating 10 sticks into 0 groups, no matter how many sticks you put in each group, at the end you have 0 groups, and hence 0 sticks; and thus no solutions making it undefined.

[Anonymous No.14829333]

>>14828352
then what is it nigger? and I meant the problem was not the analogy that multiplication is like repeated addition, but rather that you can't add things that are "infinite", e.g. irrational numbers

[Anonymous No.14829340]

>>14829333
You are quite literally retarded.

[Anonymous No.14829379]

>>14823545
>But then division is often taught as the opposite of multiplication: repeated subtraction. This
What the fuck?

[Anonymous No.14829440]

Gwaihir already answered the question yesterday. What are your u niggers still arguing for?

[Anonymous No.14829441]

>>14829440
In my country we call them Mayates; it's a type of dung beetle that you see fighting on the porch all day

[Anonymous No.14829468]

>>14829340
why? got filtered by irrational numbers?

[Anonymous No.14829491]

>>14829468
No, but I guess you did, since you can't seem to wrap your head around how they refute the concept of multiplication being repeated addition.

[Anonymous No.14829545]

>>14829491
How?

[Anonymous No.14830168]

>>14823545
Multiplication is a quicker way to add
Division is splitting a whole into parts
Subtraction is removal of a whole or part
Addition is part with part, part with whole, whole with whole
Where is the 'merge' distinction?
Diffusion is division/splitting.
What is the opposite of diffusion?

[Anonymous No.14830172]

>>14823871
Absolute bullshit. You can put a spin on anything through interpretation.

[Anonymous No.14830177]

>>14823545
Multiplication is a scaling operation. Now close this thread for wasting other's time

[Anonymous No.14831470]

>>14830177
what about division? why can't you scale by 0

[Anonymous No.14831476]

>>14830168
>What is the opposite of diffusion?
concentration?