/sci/ - Science & Math » Thread #12889909

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Anonymous Sat 27 Mar 10:47:39 2021 No.12889909 View Reply Original Report

Quoted By: >>12889961 >>12889985 >>12890015 >>12891695 >>12891761 >>12891771 >>12891806 >>12893015 >>12893047 >>12893152 >>12893258 >>12894639 >>12895936 >>12895941 >>12899546

why is division by zero undefined? why don't mathematicians just define it?

Anonymous

Anonymous Sat 27 Mar 2021 10:56:37 No.12889937 Report

Quoted By: >>12889961 >>12893198

Because you would have to create a whole other set of axioms

smortguy

smortguy Sat 27 Mar 2021 10:59:21 No.12889945 Report

Quoted By: >>12896972

isn't zero nothing? how would you divide nothing by something

Anonymous

Anonymous Sat 27 Mar 2021 11:06:05 No.12889961 Report

Quoted By: >>12889976 >>12890085 >>12890238 >>12892810 >>12893067 >>12893094 >>12893168 >>12895182 >>12899010 >>12899430 >>12899472 >>12899982

>>12889909
>>12889937
I don't get it. If I have a pizza and divide it among zero people, I still have a pizza. Take out the "I" and there is still a pizza. So I am the same and the pizza is the same on each side. One times zero is zero and one divided by zero is one.

Anonymous

Anonymous Sat 27 Mar 2021 11:11:54 No.12889976 Report

Quoted By: >>12893031

>>12889961
this is what id think, too. i wonder what complex constraints are blocking this intuitive solution

Anonymous

Anonymous Sat 27 Mar 2021 11:14:04 No.12889985 Report

Quoted By: >>12896937

>>12889909
why are niggers so fucking ugly?

Anonymous

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Anonymous Sat 27 Mar 2021 11:14:37 No.12889986 Report

Quoted By:

Anonymous

Anonymous Sat 27 Mar 2021 11:17:33 No.12889995 Report

Quoted By: >>12892833 >>12893034

Distributive property states that for all numbers
x*(y+z)=x*y + x*z.
So
a*0 = a*(0+0)=a*0 + a*0
Subtracting a*0 from both sides we get
0=a*0.
So if division by 0 were defined, then
(1/0)*0 = 0
But also 1/0 * 0 = 1, so
0=1

Anonymous

Anonymous Sat 27 Mar 2021 11:25:18 No.12890015 Report

Quoted By: >>12893076

>>12889909
Why isn't dividing by a plus sign defined? Why don't mathematicians define it? Because it's retarded and defeats the purpose.

Anonymous

Anonymous Sat 27 Mar 2021 11:50:13 No.12890085 Report

Quoted By: >>12890104 >>12893031

>>12889961
Asking what 1 divided by zero is more like asking that if you share a pizza equally with 0 people, how much pizza each of those 0 persons gets. Makes no sense.

Anonymous

Anonymous Sat 27 Mar 2021 11:56:49 No.12890104 Report

Quoted By: >>12890122 >>12890124 >>12895750

>>12890085
Each person gets zero pizza.
1/0=0. Easy.

Anonymous

Anonymous Sat 27 Mar 2021 12:01:00 No.12890122 Report

Quoted By:

>>12890104
but there are no people, so no-one would get pizza.

Anonymous

Anonymous Sat 27 Mar 2021 12:01:34 No.12890124 Report

Quoted By:

>>12890104
>giving no pizza to no people gets you one pizza!

Anonymous

Anonymous Sat 27 Mar 2021 12:49:31 No.12890238 Report

Quoted By: >>12893031

>>12889961
if you share the pizza with 0.5 people you have two pizzas
limes would be inf

Anonymous

Anonymous Sat 27 Mar 2021 21:02:12 No.12891695 Report

Quoted By: >>12895242

>>12889909
It is defined. It is defined as 'undefined'.

Anonymous

Anonymous Sat 27 Mar 2021 21:19:09 No.12891761 Report

Quoted By:

>>12889909
because the potential number a/0 would necessarily have such shitty properties that you couldn't use it in any sort of arithmetic anyway. basically all you can do is to ad hoc define it as something and that's about it.
plot twist: that's exactly we do actually, the value is called "undefined"

Anonymous

Anonymous Sat 27 Mar 2021 21:23:22 No.12891771 Report

Quoted By:

>>12889909
>Why dont mathematicians define it
In analysis its not defined because it leads to a lot of problems (2/0=1/0 for exanple), but in some branches of math (projective geometry in particular) it is defined.

Anonymous

Anonymous Sat 27 Mar 2021 21:35:45 No.12891806 Report

Quoted By:

>>12889909
Because you want it to be reversible. We usually define a/b as the number that gives a when you multiply it with b. Therefore 1/0 would need to be the number that gives 1 when multiplied with 0.

Anonymous

Anonymous Sun 28 Mar 2021 03:48:21 No.12892810 Report

Quoted By: >>12893031

>>12889961
So you're telling me this function has value 1 at x=0?

Anonymous

Anonymous Sun 28 Mar 2021 04:00:08 No.12892833 Report

Quoted By:

>>12889995
Why are you saying that dividing by zero is a problem when 0/0 is a bigger one

Anonymous

Anonymous Sun 28 Mar 2021 05:43:29 No.12893015 Report

Quoted By: >>12893041

>>12889909
I hereby define it to be 3, no more and no less.

Anonymous

Anonymous Sun 28 Mar 2021 05:51:33 No.12893031 Report

Quoted By:

>>12890085
Very helpful. Thank.
>>12890238
Whoa!
>>12889976
Muh bro
>>12892810
I'm just telling you that I am a dummy. Don't over think it or I can't hang with you.

Anonymous

Anonymous Sun 28 Mar 2021 05:54:57 No.12893034 Report

Quoted By: >>12893249

>>12889995
>0=a*0.
Fine.
>(1/0)*0 = 0
Nigger did you just have an aneurysm? That doesn't follow.

Anonymous

Anonymous Sun 28 Mar 2021 06:00:24 No.12893041 Report

Quoted By:

>>12893015
tree fiddy

Anonymous

Anonymous Sun 28 Mar 2021 06:02:21 No.12893047 Report

Quoted By: >>12893057

>>12889909
Division is just subtraction until you get 0. 20/5 = 20 - 5 = 15 - 5 = 10 - 5 = 5 - 5 = 0. Count the number of times you subtracted and theres your answer. If you 20/0 then you get 20 - 0 on and on.

Anonymous

Anonymous Sun 28 Mar 2021 06:05:31 No.12893057 Report

Quoted By:

>>12893047
So then 0/0 is well-defined and equal to 1. Or 0.

Anonymous

Anonymous Sun 28 Mar 2021 06:11:26 No.12893067 Report

Quoted By: >>12893078 >>12896976

>>12889961
There isn't an I because it's zero retard. Nobody exists and nothing matters other than that pizza

Anonymous

Anonymous Sun 28 Mar 2021 06:16:52 No.12893076 Report

Quoted By:

>>12890015
You are a retard and will never be a genius mathematician

Anonymous

Anonymous Sun 28 Mar 2021 06:17:41 No.12893078 Report

Quoted By:

>>12893067
Maybe the I is what you are overlooking. You can't wrap your head around me+pizza and, somehow, I'm the retard? Lol! Okay bro. I hope you get the hiccups.

Anonymous

Anonymous Sun 28 Mar 2021 06:24:31 No.12893094 Report

Quoted By: >>12893109

>>12889961
Mathematics is but the logical chain drawn from its axioms. You can't go to your physical intuitions for insights about it. Or at the very least, you can't weigh your intuition above what the axioms administer. Don't get filtered anon.

Anonymous

Anonymous Sun 28 Mar 2021 06:32:21 No.12893109 Report

Quoted By:

>>12893094
Ok but I wouldn't know that if you didn't explain it so well. I'd do it for you if I see you being dumb.

Anonymous

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Anonymous Sun 28 Mar 2021 06:59:56 No.12893152 Report

Quoted By: >>12893213 >>12895144 >>12895200 >>12899608

>>12889909
Teacher here.
This is why:

>6 x 2 = 12
This basically says: How much is two sixes? Twelve. Two sixes add up to twelve.

>6 ÷ 2 = 3
This basically says: How many twos does 6 contain? Three. 6 contains three twos.

>6 ÷ 0 = ?
This basically says: How many zeroes does six contain? The answer is effectively: Infinite.

Zeroes have no value, they signify nothing. You can fit infinite nothings into any number, so anything divided by zero is infinity, and there's no nice way for a standard LCD calculator to display a different version of infinity for every/any number you might divide by zero.

>why don't mathematicians just define it?
Yeah, sure, let's just make up some random number to replace this value that is currently beyond human comprehension, that's totally how math works.

Anonymous

Anonymous Sun 28 Mar 2021 07:08:00 No.12893168 Report

Quoted By: >>12895180

>>12889961
without U around that pizza will definitely disappear. trust me

Anonymous

Anonymous Sun 28 Mar 2021 07:36:46 No.12893198 Report

Quoted By: >>12894732

>>12889937
so? create it. What do we even pay you for?

Anonymous

Anonymous Sun 28 Mar 2021 07:44:46 No.12893213 Report

Quoted By:

>>12893152
>Yeah, sure, let's just make up some random number to replace this value that is currently beyond human comprehension, that's totally how math works.
yes, that's how math works

Anonymous

Anonymous Sun 28 Mar 2021 08:16:54 No.12893249 Report

Quoted By:

>>12893034
a=(1/0)

Anonymous

Anonymous Sun 28 Mar 2021 08:23:04 No.12893258 Report

Quoted By:

>>12889909
they defined it as undefined duh

Anonymous

Anonymous Sun 28 Mar 2021 18:16:37 No.12894639 Report

Quoted By:

>>12889909
1/0 is the pre-image of a mobius transformation (such as z -> 1/z) at the north pole of the Riemann Sphere. It's literally well defined in the form of the extended complex plane.

Anonymous

Anonymous Sun 28 Mar 2021 18:19:24 No.12894651 Report

Quoted By: >>12894726 >>12899111

1/0 is the image of a mobius transformation (such as z -> 1/z) at the pole of the transformation (in this case z = 0), it corresponds to the north pole of the riemann sphere. It's literally well defined in the context of the extended complex plane.

https://en.wikipedia.org/wiki/M%C3%B6bius_transformation

Anonymous

Anonymous Sun 28 Mar 2021 18:36:58 No.12894726 Report

Quoted By: >>12899111

>>12894651
To add on to this, if we have a particular mobius transform $T(z) = \frac{az + b}{cz + d}$ , then we define $\infty$ such that $T\left( \frac{-d}{c} \right) = \infty \\ T^{-1}(\infty) = \frac{-d}{c}.$ Hence, infinity is only well defined for a specific transform.

Anonymous

Anonymous Sun 28 Mar 2021 18:38:20 No.12894732 Report

Quoted By:

>>12893198
https://en.wikipedia.org/wiki/Wheel_theory

Anonymous

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Anonymous Sun 28 Mar 2021 20:19:21 No.12895144 Report

Quoted By:

>>12893152
>>why don't mathematicians just define it?
>Yeah, sure, let's just make up some random number to replace this value that is currently beyond human comprehension, that's totally how math works.
Blocks your path

Anonymous

Anonymous Sun 28 Mar 2021 20:28:56 No.12895180 Report

Quoted By:

>>12893168
*Crust me*
Fixed.

Anonymous

Anonymous Sun 28 Mar 2021 20:30:00 No.12895182 Report

Quoted By:

>>12889961
Nope the pizza will be the reminder.

Anonymous

Anonymous Sun 28 Mar 2021 20:33:56 No.12895200 Report

Quoted By:

>>12893152
Lol, You forgot to mention the fact that there is also grouping division and share division.

Anonymous

Anonymous Sun 28 Mar 2021 20:45:38 No.12895242 Report

Quoted By:

>>12891695
no it isn't
"undefined" is placeholder/variable
gauss managed to finally define "1" as a unit only about 200 years old, but the lack of a definition didn't prevent previous generations of mathematicians from making discoveries.
divided by zero is undefined because nobody has done for it what gauss did for 1.

Anonymous

Anonymous Sun 28 Mar 2021 22:53:48 No.12895750 Report

Quoted By:

>>12890104
no you're wrong.
each person has 2 pizza, or 3, or 4, it doesn't matter as there is noone anyway.
this is what undefined means.

Anonymous

Anonymous Sun 28 Mar 2021 23:33:07 No.12895936 Report

Quoted By:

>>12889909
How much pizza do you need to give x people so that you have no pizza left after you gave everyone their share? 1/x of a pizza per person.

Now imagine x=0, how much pizza do you need to give 0 people so that you have no pizza left?

Anonymous

Anonymous Sun 28 Mar 2021 23:34:36 No.12895941 Report

Quoted By:

>>12889909
Why dont you just define it? Write a short paper and post online. Literally all it takes. Theres no math pope to make it canonical.

Anonymous

Anonymous Mon 29 Mar 2021 06:14:46 No.12896937 Report

Quoted By:

>>12889985
I have a theory that racists are faceblind.
Dude literally sees an image of an obvious caricature and believe's it's a real face. It's probably why they think blacks look like gorillas too.

Anonymous

Anonymous Mon 29 Mar 2021 06:24:30 No.12896972 Report

Quoted By: >>12897020

>>12889945
The same way you make something out of nothing upon nothing. 0^0=0!=1, but in reverse.

Anonymous

Anonymous Mon 29 Mar 2021 06:25:32 No.12896976 Report

Quoted By:

>>12893067
Then it isn't just 1 unit, it is one unit of infinity.

Anonymous

Anonymous Mon 29 Mar 2021 06:26:00 No.12896978 Report

Quoted By: >>12897014

It creates too many problems, as some anons have pointed out. A related question is why don't we define +infinity or -infinity as numbers? You actually can without too many issues. Useful for measure theory: https://en.wikipedia.org/wiki/Extended_real_number_line

You may benefit from comparing this system to one where division by 0 is defined. Maybe make 1/0 = infinity as a starting point.

Anonymous

Anonymous Mon 29 Mar 2021 06:44:36 No.12897014 Report

Quoted By:

>>12896978
Can infinity interact with numbers in traditionally numeric ways?
What is infinity minus one?
Is infinity a prime number or does it have other factors?

Anonymous

Anonymous Mon 29 Mar 2021 06:46:46 No.12897020 Report

Quoted By: >>12897021 >>12897053

>>12896972
>0^0
Indeterminate.
>0!
Empty product is the multiplicative identity.

Anonymous

Anonymous Mon 29 Mar 2021 06:48:55 No.12897021 Report

Quoted By: >>12897026

>>12897020
>Empty product
If that is what you want to call it, that is your answer.

Anonymous

Anonymous Mon 29 Mar 2021 06:51:06 No.12897026 Report

Quoted By: >>12897047

>>12897021
Yeah, it's just what I want to call it
https://en.wikipedia.org/wiki/Empty_product

Anonymous

Anonymous Mon 29 Mar 2021 06:58:52 No.12897047 Report

Quoted By:

>>12897026
Obviously since there are numerous ways to refer to it as listed on that page (nullary product, vaccuous product, empty set, null set, etc), but no matter which precise term you want for it, that is the mathematical definition of something that it is assumed nothing is divided into.

Anonymous

Anonymous Mon 29 Mar 2021 07:02:02 No.12897053 Report

Quoted By: >>12897070

>>12897020
>Indeterminate.
None of the calculators I use have any problem determining 0^0, even window's and android's shitty built in calculator determines the value to be 1.

Anonymous

Anonymous Mon 29 Mar 2021 07:05:56 No.12897066 Report

Quoted By:

If there were a single reasonable way to define division by zero, then it would certainly make sense to do it. Division by zero could result in any (hyper)real number depending on the circumstances, so it is easier to leave it undefined.

Anonymous

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Anonymous Mon 29 Mar 2021 07:07:56 No.12897070 Report

Quoted By: >>12897082 >>12897087

>>12897053
Maybe if you're considering something like x^x, but try another function and it gets very muddy

Anonymous

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Anonymous Mon 29 Mar 2021 07:10:32 No.12897082 Report

Quoted By: >>12897087

>>12897070
Incidentally, if you use $| \ln x|$ , you get 1/e

Anonymous

Anonymous Mon 29 Mar 2021 07:12:06 No.12897087 Report

Quoted By: >>12897104

>>12897070
>>12897082
If you put in a function like natural log that is specifically not defined for x=0, of course it won't make sense when x=0, try a function that doensn't have the caveat of x>0.

Anonymous

Anonymous Mon 29 Mar 2021 07:22:15 No.12897104 Report

Quoted By: >>12897120

>>12897087
I don't know what to tell you if you think limits at indeterminate forms don't behave weirdly
There are more examples here https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero
I know this does't necessarily support my point somewhat since it also says 0^0 = 1 in an algebraic sense, but it's significantly more dubious than 0!

Anonymous

Anonymous Mon 29 Mar 2021 07:29:31 No.12897120 Report

Quoted By:

>>12897104
I didn't say it wasn't messy, counterintuitive to the point of paradoxical, and thus confusing, I said that is the widely accepted mathematical definition for how something results from nothing and thus how you can divide nothing by something due to the widespread logical utility of the definition.

Anonymous

Anonymous Mon 29 Mar 2021 18:44:15 No.12899010 Report

Quoted By:

>>12889961
Once you define 1/0=1 you can prove that 1=2 and then you've broken math

Anonymous

Anonymous Mon 29 Mar 2021 19:14:30 No.12899111 Report

Quoted By: >>12899353

>>12894651
>>12894726
this stuff is too high-level for /sci/, anon. let the people keep arguing about their elementary school paradoxes

Anonymous

Anonymous Mon 29 Mar 2021 20:12:48 No.12899353 Report

Quoted By:

>>12899111
Mobius transforms are not high level

Anonymous

Anonymous Mon 29 Mar 2021 20:34:53 No.12899430 Report

Quoted By: >>12899449

>>12889961
>muh irl analogies
this is not math

Anonymous

Anonymous Mon 29 Mar 2021 20:43:53 No.12899449 Report

Quoted By: >>12899462 >>12899509

>>12899430
those analogies are literally the only reason math was invented in the first place

Anonymous

Anonymous Mon 29 Mar 2021 20:48:16 No.12899462 Report

Quoted By: >>12899483

>>12899449
And writing was first invented as an accounting tool. Does that mean that according to your logic poetry shouldn't be a thing? Mathematics exists on its own, regardless of what engineerfags think.

Anonymous

Anonymous Mon 29 Mar 2021 20:51:57 No.12899472 Report

Quoted By:

>>12889961
think of it as a jar that holds one of something, how many times can you put zero of that thing into it? you could spend your whole life putting nothing into the jar, every second of every day, and at the end of your life the jar is still empty.

Anonymous

Anonymous Mon 29 Mar 2021 20:55:12 No.12899483 Report

Quoted By: >>12899497

>>12899462
according to my logic?
you're the one saying that irl analogies are not math lmao

Anonymous

Anonymous Mon 29 Mar 2021 21:00:03 No.12899497 Report

Quoted By: >>12899502

>>12899483
Yes, you logic is
>hurr durr the purpose of math was to be an irl analogy at first
>therefore by the same logic the purpose of writing must be purely accounting and nothing else, because first writing's purpose was accounting
Do you ask your favorite question "how's that gonna help me in life/How's that practical" when you go to a movie theater or an art gallery? You appliedfags must be the most boring fucking people on the planet if everything in life must be about your utilitarian "application".

Anonymous

Anonymous Mon 29 Mar 2021 21:00:57 No.12899501 Report

Quoted By: >>12899531

let's define zero:
1 * 0 = 2 * 0 -> 1/2 = 0/0
3 * 0 = 4 * 0 -> 3/4 = 0/0
then 0/0 = 1/2 and 0/0 3/4
how can you handle with this?

Anonymous

Anonymous Mon 29 Mar 2021 21:01:43 No.12899502 Report

Quoted By: >>12899509 >>12899526

>>12899497
literally never said that the purpose of a subject needed to be purely one thing or the other

Anonymous

Anonymous Mon 29 Mar 2021 21:04:17 No.12899509 Report

Quoted By: >>12899512 >>12899526

>>12899502
>>12899449
yes, you did
>those analogies are literally the only reason math was invented in the first place
Math is not about silly pizza analogies. It's about axioms and definitions, and building a theory analytically from those. Same way modern writing is not about counting how many bushels of wheat there are in a barn, it has evolved past that notion to a something much more abstract and beautiful like poetry.

Anonymous

Anonymous Mon 29 Mar 2021 21:05:15 No.12899512 Report

Quoted By: >>12899523 >>12899526

>>12899509
>is a poetryfag
what a surprise

Anonymous

Anonymous Mon 29 Mar 2021 21:07:29 No.12899523 Report

Quoted By:

>>12899512
sorry for not being the most robot-like person. I like art and music. Again, I will repeat
>Do you ask your favorite question "how's that gonna help me in life/How's that practical" when you go to a movie theater or an art gallery?
You probably never even went to an art gallery in your life with such an outlook on life.

Anonymous

Anonymous Mon 29 Mar 2021 21:09:04 No.12899526 Report

Quoted By:

>>12899502
>>12899512
samefagging to make >>12899509 feel he's alone discussing with other 2
good job

Anonymous

Anonymous Mon 29 Mar 2021 21:10:03 No.12899531 Report

Quoted By:

>>12899501
The additive and multiplicative absorptive properties are not supported in any way by logic

Anonymous

Anonymous Mon 29 Mar 2021 21:17:32 No.12899546 Report

Quoted By: >>12899594 >>12899702 >>12899715

>>12889909
Zero doesn't have a multiplicative inverse. You could make something up, but it wouldn't be algebraically nice whatever you pick.

Anonymous

Anonymous Mon 29 Mar 2021 21:28:56 No.12899594 Report

Quoted By:

>>12899546
Ask Tooker about it

Anonymous

Anonymous Mon 29 Mar 2021 21:31:32 No.12899608 Report

Quoted By:

>>12893152

Also tack on that the concepts of these numbers is a thought to quantify something from the physical world. Counting came from our physical reality. I have one barley seed, now two, now three, ad infinitum. People forget the basics now and days.

Anonymous

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Anonymous Mon 29 Mar 2021 21:56:44 No.12899702 Report

Quoted By:

>>12899546
it works nicely in the context of the mobius transformation $T(z) = \frac{1}{z}$ acting on the extended complex plane if you define $\infty \text{ such that } T(0) = \infty, T^{-1} (\infty) = 0 \implies \infty * 0 = 1.$ It doesn't lead to contradictions like 1 = 2 since infinity is only the image of your simple pole.

Anonymous

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Anonymous Mon 29 Mar 2021 21:59:58 No.12899715 Report

Quoted By: >>12899754

>>12899546
it works nicely in the context of the mobius transformation $T(z) = \frac{1}{z}$ acting on the extended complex plane if you define $\infty = T(0)$ , $T^{-1} (\infty) = 0 \implies \infty * 0 = 1.$ It doesn't lead to contradictions like 1 = 2 since infinity is only the image of your simple pole.

Anonymous

Anonymous Mon 29 Mar 2021 22:06:31 No.12899754 Report

Quoted By:

>>12899715
* It doesn't lead to contradictions like 1 = 2 since infinity is only defined in the context of a specific mobius transformation and its simple pole, to get something like $\infty * 0 = 2$ we would have to use the map $T(z) = \frac{2}{z}$ .

Anonymous

Anonymous Mon 29 Mar 2021 22:55:40 No.12899982 Report

Quoted By:

>>12889961
I am the pizza.

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