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drunkbnu

Formerly HG

Joined: 2017-08-16

Posts: 2,306

Math

Do you want to talk about math? Do it here

I've been very confused with division by 0. So i decided to ask you what 1/0 is

What would be your answer to this math operation?

▼My answer

Undefined

1/0 gives an infinity after the denominator decreases to 0, increasing the final result until it becomes unreachable. If denominator is positive, the result is a positive infinity. If denominator is negative, the result is a negative infinity. But if 0 is a neutral (+/-) value, the infinity polarity is unknown. Meaning that it can be a positive infinity or a negative infinity. Which one should be chosen?
The answer is Undefined

Gosha

Member

From: Russia

Joined: 2015-03-15

Posts: 6,211

Re: Math

You cant divide by 0 because :
lets do some work

5 x 4 = 20 right?
20 : 4 = 5, 20 : 5 = 4 .

But

5 x 0 = 0
You cant get 5 when you divid 0 by 0.

0 : 0 =/= 5.
or it is = ?

It means if we divid 0 by 0 we can get 5 or anything like 1, 2 , 3, 4 etc

Also 0 is not negative or positive number, it is nothing.
thats why we also can get -1, -2, -3, -4 etc

so

X : 0 = Infinity. Infinity infinity. with all numbers what even possible.

drunkbnu

Formerly HG

Joined: 2017-08-16

Posts: 2,306

Re: Math

You cant divide by 0 because :
lets do some work

5 x 4 = 20 right?
20 : 4 = 5, 20 : 5 = 4 .

But

5 x 0 = 0
You cant get 5 when you divid 0 by 0.

0 : 0 =/= 5.
or it is = ?

It means if we divid 0 by 0 we can get 5 or anything like 1, 2 , 3, 4 etc

Also 0 is not negative or positive number, it is nothing.
thats why we also can get -1, -2, -3, -4 etc

so

X : 0 = Infinity. Infinity infinity. with all numbers what even possible.

The answer to that is that 0 * infinity = 1 after 1/0 = infinity and 1/infinity = 0

0 * infinity = 1?

Doing that operation is exactly like doing 0/0. You will get different results according to the formats and laws you use.
You can divide by 0 as x/0 = infinity and x/infinity = 0. But 0*infinity is an indeterminate form here.
0/0 is an indeterminate forum because it can give 1, 0 or an infinity. Same happens with 0*infinity. It can give 1 after x*1 / x = 1 when x = 0

Prodigy

Member

From: The United States of America

Joined: 2015-07-15

Posts: 2,613

Re: Math

divided by 0 error

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Gosha

Member

From: Russia

Joined: 2015-03-15

Posts: 6,211

Re: Math

gosh, Math sucks

Zumza

Member

From: root

Joined: 2015-02-17

Posts: 4,656

Re: Math

Dividing by 0 doesn't make any sense.
But 0 divided by a number is possible and gives 0 as result.
Multiplying by 0 gives also gives 0.
I made a quick equation for you:
a = b = 1
<=> (a + b)(a - b) = 0 <=> (a + b) = 0 / (a - b) => (a + b) = 0
But a = b = 1 that means (1 + 1) = 0 => 2 = 0 which is a nonsense.

Edit: Math is one of the oldest science. If theres a rule then it is for a good reason.
For the good of men kind, please stop reinventing it.

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Gosha

Member

From: Russia

Joined: 2015-03-15

Posts: 6,211

Re: Math

Dividing number by 0 give you infinity number

and

Any number + / - / * / : on any number gives you 2 results:

a + b = c and 0
a - b = c and 0
a * b = c and 0
a : b = c and 0

or not?

Math suck anyways

Zumza

Member

From: root

Joined: 2015-02-17

Posts: 4,656

Re: Math

Dividing number by 0 give you infinity number

and

Any number + / - / * / : on any number gives you 2 results:

a + b = c and 0
a - b = c and 0
a * b = c and 0
a : b = c and 0

or not?

Math suck anyways

The divisor, in your case b, must be different from 0.
Basically: (∀) b ≠ 0, a / b = c

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Luka504

Member

From: Serbia,probs never heard of it

Joined: 2015-02-19

Posts: 2,934

Re: Math

Imagine you have 0 cookies and want to spread them with 0 friends.(you make up de one)
Makes no sense right?
Cookie monster is sad cuz there is no cookies
You are sad cuz u have no friends

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How long will it take me to get banned again?
Place your bets right here.

Gosha

Member

From: Russia

Joined: 2015-03-15

Posts: 6,211

Re: Math

Imagine you have 0 cookies and want to spread them with 0 friends.(you make up de one)
Makes no sense right?
Cookie monster is sad cuz there is no cookies
You are sad cuz u have no friends

\

I can give 5 cookies to 0 friends

every friend will get 0 cookies
#math_sucks

drunkbnu

Formerly HG

Joined: 2017-08-16

Posts: 2,306

Re: Math

Imagine you have 0 cookies and want to spread them with 0 friends.(you make up de one)
Makes no sense right?
Cookie monster is sad cuz there is no cookies
You are sad cuz u have no friends

Siri from iPhone/iPad/iPod told you that, right?
Even it says that 0/0 is indeterminate.

Converting this topic into official math topic...

Zumza

Member

From: root

Joined: 2015-02-17

Posts: 4,656

Re: Math

#MathIsLifeMathIsLove

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Bimps

Member

Joined: 2015-02-08

Posts: 5,067

Re: Math

infinity is a concept, not a number

Freckleface

Member

Joined: 2015-04-02

Posts: 1,364

Re: Math

Lets go back to basics... You have 5 things and you put in into 0 groups. 0 groups means 0 things. EZPZ

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F

Gosha

Member

From: Russia

Joined: 2015-03-15

Posts: 6,211

Re: Math

Lets go back to basics... You have 5 things and you put in into 0 groups. 0 groups means 0 things. EZPZ

I said the same thing

Imagine you have 0 cookies and want to spread them with 0 friends.(you make up de one)
Makes no sense right?
Cookie monster is sad cuz there is no cookies
You are sad cuz u have no friends

I can give 5 cookies to 0 friends

every friend will get 0 cookies
#math_sucks

Ratburntro44

Member

Joined: 1970-01-01

Posts: 1,383

Website

Re: Math

In most cases where "division" is defined as an operation it is simply multiplying by the inverse of the divisor. In order for it to be well defined, the divisor does not have an inverse. In any ring (except the ring of one element, which may not even be defined depending on the definition of ring you choose), the "additive" identity does not have a "multiplicative" inverse. Within the rings of integers, rational numbers, and real numbers given with operations + and × (standard addition and multiplication), the additive identity is the number 0. As a result, 0 does not have a multiplicative inverse, meaning that division by 0 makes no sense to be defined in the normal sense in which one would define division on a ring/field (fields being the mathematical object where division usually appears).

There are some other senses in which division could be defined. For example, instead of using anything to do with rings we could use the definition of divisibility over the integers. By this definition, a divides b if b=qa for some integer q. In order for 0 to divide 1, it would be necessary to find an integer q such that 1=q×0. However, for all integers, q×0=0, so this is impossible. Thus, 0 cannot divide 1.

Additionally, it could potentially be possible to define 1/0 specially by taking a limit using calculus. This approach is fairly similar to what is given by HG; the positive sided limit approaches positive infinity, and the negative sided limit approaches negative infinity. Since these aren't equal, there is no limit (finite or infinite) for 1/x as x approaches 0. However, even if the limit were to be positive infinity on both sides, it would not necessarily make sense to define 1/0 as positive infinity.

While it is possible to construct number systems in which infinity is a number, these systems always end up having significantly different properties from the more familiar number systems (integers, rationals, and reals). The most basic example of a number system with infinity in it would be the extended real numbers; in this case, the problem of having infinity as a number is solved by making even more potential operations undefined. It isn't a field, or even a group, and its main use is as a notational convenience in analysis.

Another system would be the real projective line, which only has a single point of infinity (rather than positive and negative ones). In fact, under this system, 1/0 actually is defined as infinity (essentially; this is a slight simplification). However, using this system leads to other complications that are not necessary or helpful for normal mathematics. Other number systems with infinity include the hyperreal numbers and the surreal numbers, used in non-standard analysis and and set theory respectively. Both of these are fields like the real numbers, and even though they have infinity don't define 1/0. They (particularly the surreals) are quite complicated to use, and for a number of reasons the real numbers are preferred for, well, most things.

Most of this information was probably not very relevant to the topic but whatever. TL;DR: in most contexts it doesn't make sense to define 1/0. In the ones where we do, it generally has to be some sort of infinity. However, treating infinity as a number adds its own complications that we don't usually want to deal with. In fact, even when we treat infinity as a number, it's usually better not to define 1/0. It just rarely makes any sense to define it.

Zumza

Member

From: root

Joined: 2015-02-17

Posts: 4,656

Re: Math

Well, indeed, concepts are a different subject.
The concept of your problem may give a ±∞.

You may be also familiar with the imaginary number concept i² = -1 By normal rules i can't exist, but however it is used.
Edit: TL;DR; its just a convenient for mathematical fiction.

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ZeldaXD

EE Homeboy

From: Cyprus

Joined: 2015-02-15

Posts: 1,539

Website

Re: Math

Daily reminder that 0.99999... is equal to 1.

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Tako

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From: Memphis, Tennessee, USA

Joined: 2015-08-10

Posts: 6,663

Website

Re: Math

Why not just use L'Hôspitál?

If you're just trying to evaluate 1/0 you're going to be in a pickle (and I think we've beat that horse into nonexistence) but if instead you have a limit which approaches x/0 or inf/0 or something like that, then you can use L'Hôspitál to reveal the actual answer.

An example:
lim x->0 [sin(x)/x] => 0/0
lim x->0 [sin(x)/x] == lim x->0 [cosx/1] == 1

This also demonstrates why x/0 needs to be undefined. Notice in the first statement I said => 0/0 instead of == 0/0. If I said it equals 0 then I could then say

lim x->0 [sin(x)/x] == 0/0
lim x->0 [2x/x^2] == 0/0

therefore

sin(x)/x == 2x/x^2
1 == 2

which is definitely false.

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Since this is now the "official" math topic (and I am a math major #jealous?) I'd like to transition into something far more fascinating than illogical division. This idea of indeterminate forms having actual values is found elsewhere. Riemann unintentionally discovered this with his Zeta function.

ζ(s) = Σ(n=0, inf) [1/n^s]

This is essentially the sum of all the inverses raised to the power n.

This is super cool because you can use analytic continuation to find values for negative numbers.

What happens when you plug in negative numbers?

ζ(-1) = 1 + 2 + 3 + 4 + ...

You can see how this series goes to infinity. However, if you "remove" the infinite part of this function via analytic continuation, you get an incredibly fascinating answer: -1/12.

Negative one twelfth.

This answer might seem "stupid" but it is quite legitimate if you think of the series not in terms of simple addition but as an infinite sum, outside the bounds of what we can comprehend.

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Yeah, well, you know that's just like, uh, your opinion, man.

Onjit

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Joined: 2015-02-15

Posts: 9,709

Website

Re: Math

Five times nine is at least forty

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:.|:;

drunkbnu

Formerly HG

Joined: 2017-08-16

Posts: 2,306

Re: Math

Five times nine is at least forty

5a = 45 if a=9

Gosha

Member

From: Russia

Joined: 2015-03-15

Posts: 6,211

Re: Math

Five times nine is at least forty

5a = 45 if a=9

nine may be + and -

it means
5a = b
If a = 9 , b = 45
If a = -9 , b = -45

5a = +-45

Onjit

Member

Joined: 2015-02-15

Posts: 9,709

Website

Re: Math

Five times nine is at least forty

5a = 45 if a=9

nine may be + and -

it means
5a = b
If a = 9 , b = 45
If a = -9 , b = -45

5a = +-45

5 x 9 >= 40

Also, Rick and Morty.

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:.|:;

Freckleface

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Joined: 2015-04-02

Posts: 1,364

Re: Math

whats square root of -4?

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F

Bimps

Member

Joined: 2015-02-08

Posts: 5,067

Re: Math

whats square root of -4?

2i