When I divide something what's actually happening?
>>7665926
You're dividing it. Separating one whole into multiple constituent parts.
What does that REALLY mean? We don't know. We just don't know. We only understand it on certain scales.
>>7665926
You're multiplying by its inverse
You're repeatedly subtracting
200/10 =20 because you can subtract 10, 20 times from 200.
It's not that difficult really
explain why a^0 = 1
>>7666357
Because a^0 = a^(n-n) = a^n / a^n = 1
>>7666371
thats neat
In the most moral sense, you are taking an object and "quotienting out" some subobject. The same thing happens when you take a group and quotient out a subgroup. You are pretty much dividing by that object. If we look only at the natural numbers and view division as being only partially defined (for numbers that will divide evenly), we can recover normal division from the idea above. Take the term 4/2: we have a 4-element cyclic group, and we want to quotient out an order-2 cyclic subgroup. So, we take a new group of cosets of elements in our chosen subgroup, and now we have a 2-element group! Z4/Z2=Z2.
Now let's look at compact manifolds. We start with the 2-disk, which is just diffeomorphic to the closed unit ball in R^2. Now, we have that every compact manifold has a (possibly empty) boundary. So, we want to "divide" our disk by its boundary (which is the subspace consisting of just the points of the unit circle, if you want to think of it with coordinates). For compact manifolds (and in general, topological spaces), quotienting out a subspace involves crushing it down to a single point, while preserving continuity of course. So if we crush the boundary of a disk down to a point, we get a 2-sphere! Neat-o.
Division is a very prevalent idea in mathematics.
>>7666488
If you don't want to be anonymous, don't visit 4chan.
>>7666509
Whoa, you sure told me! Why does the site have that field available to posters if it should never be touched?
>>7666768
Nice meme.
>>7666785
Nice lack of a valid retort.
>>7666339
This
>>7666488
FUCKING NECKBEARDS GET THE FUCK OFF MY BOARD REEEEEEEEEEEEEEEEEEEE
>>7665926
You are finding the ration of two objects to a unit object.
What number has the same ratio to 2 and 3 that 2 and 3 have to 1? 6.
This applys to numbers, vectors, tensors, etc.
>>7665926
X/Y is breaking X up into y groups such that the amount of groups becomes our new atomic particle or the thing being described by our number. So if X/Y=Z you're stating that if you break up X into Y groups you'll have Z items afterwards where an item is a filled group. When you have decimals you end up with unfilled groups to express the remainder as R/Y. This is also why 0/0 is undefined, because there are infinite solutions that satisfy the equation such that z cannot be graphed or expressed on any finite amount of paper or space in any way other than saying "literally anything".
>>7666339
This definition of division ONLY applys to real numbers, and is not universal.
The broader definition of division is multiplication of an inverse, and the definition of multiplication is >>7666911
The operations, addition, multiplication and exponentiation can be simplified to arithmetic for real numbers, however those definitions are not universal. Exponentiation, even for numbers, does not have the same properties of as multiplication. For example, it does not distribute. (2 + 5)^2 is not the same as (2^2 + 5^2), therefore exponentiation is not just "repeated multiplication". Similarly, multiplication of two square matrices is not simply adding the matrices.
>>7666509
I could not help but notice your png was not optimized anon.
I have optimized your png.
Your png is now optimized.
>>7667039
based png optimizer at it again
>>7667039
How do you even spot things like that?
You're mulitplying an element a with the inverse of an element b.
>>7667039
It's too bright now
5^3 = 125
5^2 = 25
5^1 = 5
125/5 = 25
25/5 = 5
5/5 = ? ? ?
profit
lets assume x is the result of a/b. for convenience we will also assume that a/b is an integer. purely by definition of the division we are looking for the result of this x in the following eqaution a- x*b = 0. so what we are actually looking for is how many times can i subtract b from a. division is actually just a definition, like everything in math.
>>7667114
>>7667120
Hm, seems they are. I didn't visually verify the output myself, and I guess this is one more reason to not use imagemagick to verify decoded outputs are perceptually identical. It seems it ignores cHRM and gAMA chunks (which specify gamma and chromaticity for color primaries on display). Both of which seemed to have been stripped, despite everything explicitly being set not to.
Sorry anon, your png was not truly optimized. Might re-optimize later.
>>7666371
Prove that a^(n-n) = a^n/a^n
>>7667039
>optimized
>298 bytes of bloat
>>7667039
https://www.youtube.com/watch?v=TaVtmrJsOlQ&t=2m42s
>>7667120
Well shit I've never encountered this before, but technically >>7667039 is still optimized losslessly, it just doesn't have the gamma correction imbedded into the .png. I redid his with that left intact, I haven't seen it but let's see if it still works.
Truth be told if I was actually optimizing it I would rip out all of the correction chunks anyway.
>>7667356
a^(n-n) = a^n * a^(-n) = a^n/a^n
>>7667039
>that
>optimized
>>7668927
pussy you need to dare to step into the void
>>7668927
>lossy
Try again
>>7666768
Gee, I wonder why they call this place an anonymous image board. Maybe they just put in the tripcodes for boards like /soc/ and assumed people wouldn't be as retarded to go and use it on other boards.
If you are desperate for a reputation, try facebook.
How would i divide X by Y whilst only using + or - and only using whole numbers?
>>7665926
Something is branching into another something to it's limit, the separating them, like a parasite
What you should really be asking OP is what the conditions on the numbers that are being used in division are
>>7669262
If X is divisible by Y you can use the following algorithm:
If X>Y
X=X-Y
>>7665941
bingo
Breaking the numerator into equal parts co...something, we'll say coherent of the denominator.
Breaking the numerator into equal parts coherent of the denominator.
>>7665926
Holy shit this picture just made me realize why that's the division symbol. The line is in-between, dividing, the two dots.
>>7670304
Correspondent!
*
>>7665926
You're scaling it. For complex numbers, you scale and rotate.
>>7667397
AHAHAHAHAHAHAHA
HIS CHANNEL IS ACTUALLY THE WAY HE SAID IT WOULD BE IN HIS VIDEO
OPTIMIZED
HAHA IM CRYING IN REAL LIFE
FROM A YOUTUBE VIDEO
FOR THE FIRST TIME
HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA
>>7670310
I always thought the dots were the stand ins for the numbers
since the division symbol looks like a fraction with dots being in the numerator and denomenator
>>7668927
step up senpai
You are getting one group and distributing it evenly to another
>>7670400
>>7670400
>>7670407
>>7670271
Explain.
>>7670440
It requires that Y=0. He's bullshitting you.
>>7670445
I figured something like that. I just want him to explain himself.
>>7668909
>>7670878
erry day i'm shitpostan.
Thx for the proper explaination.
>>7670904
Sure. For a more rigorous explanation:
>15 / 5 = x
>15 / 5 - 1 = x - 1
> 15 / 5 - 5 / 5 = x - 1
> 10 / 5 = x - 1
...
> 0 / 5 = x - 3
> x = 3
>>7666926
but it DOES distribite. operations distribute one order lower. so 5(2+4)=5*2+5*4 and (2*4)^5=2^5*4^5
>>7666339
This. Division is just a speedy way to do subtraction in the same vein that multiplication is a speedy way to do addition.
>>7666509
>>7667039
You are new to png optimization
>>7668927
its lossy mate
Let me present to you the real deal.
>>7672310
Did you use zopfli with lossy 8 bit mode?
You reduced the bitdepth though, which wasn't lossless. The colors are just so similar it's difficult to notice (and depends on how your image viewer deals with quantization error when displaying it on an 8 bpc screen, so it could even be visually identical).
The original was 48 bpp.
>>7672330
Caught me. I reduced the bitdepth.
>>7670271
I see not everyone understand my brilliance. Let me elaborate:
Say you want to know z = y/x
The pseudocode would look like this
If y>x
y=y-x, z=z+1
If y>x repeat
>>7665941
does that mean that division is non-commutative shorthand for a special case of multiplication?
>>7673304
>non-commutative shorthand
a/b = b\a
>>7667397
11/10
gold
>>7673304
We NEVER use the division symbol in any form in algebra because of the fact that it's ambiguous to whether we mean the left inverse or the right inverse.
>>7674540
>left inverse or the right inverse
They are the same thing in any proper algebra
>>7674540
Left 1÷b*a
Right a÷b
>>7674555
what is commutative
