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# Division

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What is division?
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>>7645341
The ratio of one object and another in a common basis
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>>7645343
Is it the most complex of arithmetic operations?
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>>7645347
No, it is an extension of multiplication, in the same way subtraction is the addition of negative numbers (addition of inverse quantities), division is multiplication by inverse quantities.
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Isn't every possible change to a number, whether it be by multiplication or division or what have you, addition?
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>>7645357
Addition, and multiplication have definitions that go beyond numbers. For example, vectors defined by a radius and angle, there is an addition and multiplication that follows the same rules as the addition and multiplication of numbers but gives different results.

Addition and multiplication are operations on objects that follow specific rules, and while they may simplifiy to arithmetic when dealing with numbers that is not true for all objects.
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>>7645365
Huh, that's interesting.
Thank you for clearing that up for me.
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OP here. Thank you for the helpful replies.
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>>7645341
Glorified Subtraction.
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>>7645418
Division cannot possibly be to subtraction what multiplication:addition, because for 3/5, for example, how would you "subtract" 5 from 3 to get .6?
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>>7645426
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>>7645426
No way you're this dumb
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how many x fit into y
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>>7645426
3/5 is equal to subtracting 0.6 from 3 five times.
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>>7645341
Reciprocal of multiplication.
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>>7645365
Pls explain
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>>7645646
TIL 3/5 = 0
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>>7645688
Since you're obviously mentally retarded I'll make this real easy for you to understand.
Let's take 20/5, which equals 4. This is the same as subtracting 4 from 20 five times.
20 -4 - 4 - 4 - 4 - 4 = 0
Same with 3/5
3 - 0.6 - 0.6 - 0.6 - 0.6 - 0.6 = 0
This doesn't mean 3/5 equals 0 as you erroneously stated, but rather that subtracting 0.6 from 3 five times equals 0. Now stop posting because you just got BTFO.
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division is chained subtraction
that's all
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>>7645341
The amount of times the negation of the dividend can be added until the result is equal to zero.
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>>7645804
divisor*
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>>7645341
The undo button for multiplication
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>>7645341
inverse multiplication
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>>7645341
Splitting.
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>>7645341
for each number a except 0,
there is a (unique) number "a^-1" surch as
a*(a^-1)=(a^-1)*a=1

where 1 is the (unique) number surch as for each b, 1*b=b*1=b.

so b/a means b*(a^-1)
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a/b

how many groups of b fit into a?

if a the area of a rectangle, and b is the length/width of the rectangle, what is the width/length of the rectangle?
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Take a class in abstract algebra, all of you, please.
Division (on real numbers) isn't really division at all as the real numbers are a field over only addition and multiplication. Divison can't be properly defined due to the presence of 0. Dividing by a is just a shorthand way of saying multiply by 1/a
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>>7645352
But inversion is a division itself right?
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>>7646393
inversion is dividing unity by the thing you're inverting
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>>7646393
a^(-1) is defined as the number such that a*a^(-1) = 1. You don't need to divide anything.
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>>7645711
This anon wen't all out

Respect
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>>7646359
You mean "multiplying by 1 divided by a"?
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>>7646393
algebraically, inversion is a group involutive automorphism.
Now assuming your group is abelian.
"division by a" could be defined as the composite morphism of multiplication by inverse of a.

>>7646359
>Division (on real numbers) isn't really division at all as the real numbers are a field over only addition and multiplication.
????
>Divison can't be properly defined due to the presence of 0.
It can, but it requires to use Projective line. Define inf = 1/0. Then 1/inf = 0, and for any a in R, a+inf = (a*0+1)/0=1/0=inf, as one would imagine.
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File: 1436157312981.png (156KB, 549x349px) Image search: [iqdb] [SauceNao] [Google]
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>2015
>saying "division" instead of just multiplication by an inverse
>shiggydoo
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>>7645341
>>7645341
If everyone eats the same amount of pizza. how many slices can everyone get.
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>>7646530
You didn't answer the first question, and as you well know inf is not a value in R
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>>7646506
"1/a" is just notation used for a multiplicative inverse.
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>>7646530
>algebraically, inversion is a group involutive automorphism.
I just had a taste of abstract algebra this semester. I can't fucking wait to sound this pretentious to laymen.