Questions about dividing by 0

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Arr0w

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Arr0w

#1 h Dec 2, 2020, 5:00 PM • 2 Y

Y by mobro, DDCN_2011

I have a couple of questions all of which have to do with dividing by 0. Thanks in advance.
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5

This post has been edited 1 time. Last edited by Arr0w, Dec 2, 2020, 5:02 PM

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Math2k06

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Math2k06

#2 h Dec 2, 2020, 5:06 PM • 3 Y

Y by Mango247, Mango247, Mango247

$1/0$ is not a number.For #3, since anything times $0$ is $0$ , the answer should be $0$ .

Tldr don't poke into questions including $0$ and division. You will open a parallel univeerse

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aaja3427

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aaja3427

#3 h Dec 2, 2020, 5:07 PM

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S2

@above that wouldn't be true since you are multiplying by undefined. Anything to do with undefined is undefined.

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mop

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mop

#4 h Dec 2, 2020, 7:17 PM

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Undefined numbers are a class of their own. Thus, they cannot be used with real or imaginary numbers without creating an undefined result.

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cubingsoda

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cubingsoda

#5 h Dec 2, 2020, 7:22 PM • 3 Y

Y by Mango247, Mango247, Mango247

see this video

He divides $a - b$ but since $a=b$ he divides by $0$ . He gets $1=2$ !

Dividing by $0$ opens the black hole

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correcthorsebatterystaple

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correcthorsebatterystaple

#6 h Dec 3, 2020, 1:00 AM

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Yeah, there are a couple of constructs in higher maths which assign a value to 1/0 (sort of like $i$ ) but you have to bend the rules of arithmetic a bit and what's going on here (1-3) is definitely not that. They're not that useful, either. We leave 1/0 undefined most of the time, similar to how you would say "no solutions" if you were asked to solve $x^2=-1$ over $\mathbb{R}.$ (to answer 5)

An "undefined value" has no numerical value; I think even calling it a "value" in the first place is a bit of a misnomer.

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ihatemath123

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ihatemath123

#7 h Dec 3, 2020, 1:03 AM

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S4

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cubingsoda

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cubingsoda

#8 h Dec 3, 2020, 2:13 AM

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undefined = no answer so no solution

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SteindorfStrongGirl

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SteindorfStrongGirl

#9 h Dec 14, 2023, 1:18 AM

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i made a presentation on this at school :< its something about 1≠2

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Awesome_Twin1

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Awesome_Twin1

#12 h Dec 14, 2023, 1:42 AM

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1. Avoid double posting
2. Don't bump this thread. Just look at A Letter to MSM which has been pinned.

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A_MatheMagician

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A_MatheMagician

#13 h Dec 14, 2023, 1:43 AM

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please read this post first
sry @above sniped me

This post has been edited 1 time. Last edited by A_MatheMagician, Dec 14, 2023, 1:45 AM

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vrondoS

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vrondoS

#14 h Dec 14, 2023, 1:48 AM

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In some ways, you can think $\frac{1}{0}=\infty$ . This isn't rigorous, however, because then $\frac{2}{0}=2\infty=\infty$ . Thinking about it this way can help explain some of the questions you had.

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A_MatheMagician

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A_MatheMagician

#16 h Dec 14, 2023, 2:31 AM

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Post #14 by vrondoS
infinity is not a value
that does not make any sense

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ZekeMath

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ZekeMath

#17 h Dec 14, 2023, 3:07 AM

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If it's undefined, eventually somebody will define it

I say better now than later.

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Yummo

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Yummo

#18 h Dec 14, 2023, 3:08 AM

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Awesome_Twin1 wrote:

1. Avoid double posting
2. Don't bump this thread. Just look at A Letter to MSM which has been pinned.

A_MatheMagician wrote:

please read this post first
sry @above sniped me

Do you realize who posted that? @Arr0w, I thought you left AoPS a while ago.

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mathboy282

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mathboy282

#20 h Dec 14, 2023, 3:33 AM

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vrondoS wrote:

In some ways, you can think $\frac{1}{0}=\infty$ . This isn't rigorous, however, because then $\frac{2}{0}=2\infty=\infty$ . Thinking about it this way can help explain some of the questions you had.

I would argue that this isn't true. $1/0 is undefined.$ The limit of it also does not exist, because:
$\lim_{x->0^+}\frac1x = +\infty$
but also:
$\lim_{x->0^-} \frac1x = -\infty$

This post has been edited 2 times. Last edited by mathboy282, Dec 14, 2023, 3:33 AM

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JoyfulSapling

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JoyfulSapling

#21 h Dec 19, 2023, 3:09 AM

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Arr0w wrote:

I have a couple of questions all of which have to do with dividing by 0. Thanks in advance.
1
2
3
4
5

Solutions:
1
2
3
4
5

This post has been edited 4 times. Last edited by JoyfulSapling, Mar 14, 2024, 2:33 PM

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MathPerson12321

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MathPerson12321

#22 h Mar 14, 2024, 3:47 AM

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I would think a variable like b would be defined as $\frac{1}{0}$ , similar to $i$ .

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the_mathmagician

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the_mathmagician

#23 h Mar 14, 2024, 4:06 AM

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Note: defining a number like $b=\frac{1}{0}$ serves no purpose. Why did we define $i$ ? Because we created the quadratic formula and realized that we couldn't describe the full range of solutions. Plus, we found something called casus irreducibilis, in which we found that describing a root of a cubic that was a real number required the use of imaginary numbers. After we accepted that we found a lot of useful other things to do with complex numbers. As for with " $b$ ", it serves no purpose. What can we do with this? There's nothing we can do with it. Actually, all it does is completely break our current framework of math.

Edit: Also, read this by the OP, written a few years later. It's an announcement but MSM unfortunately isn't known for paying attention to those

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yummy-yum10-2021

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yummy-yum10-2021

#24 h Nov 11, 2024, 3:40 AM

Y by

Arr0w wrote:

Greetings.

I have seen many posts talking about commonly asked questions, such as finding the value of $0^0$ , $\frac{1}{0}$ , $\frac{0}{0}$ , $\frac{\infty}{\infty}$ , why $0.999...=1$ or even expressions of those terms combined as if that would make them defined. I have made this post to answer these questions once and for all, and I politely ask everyone to link this post to threads that are talking about this issue.
[...]
What about $\frac{1}{0}$ ? Suppose that $x=\frac{1}{0}$ . Then we would have $x\cdot 0=0=1$ , absurd. A more rigorous treatment of the idea is that $\lim_{x\to0}\frac{1}{x}$ does not exist in the first place, although you will see why in a calculus course. So the point is that $\frac{1}{0}$ is undefined.
[...]
What about $\frac{0}{0}$ ? Usually this is considered to be an indeterminate form, but I would also wager that this is also undefined.
[...]
INDETERMINATE VS UNDEFINED

What makes something indeterminate? As you can see above, there are many things that are indeterminate. While definitions might vary slightly, it is the consensus that the following definition holds: A mathematical expression is be said to be indeterminate if it is not definitively or precisely determined. So how does this make, say, something like $0/0$ indeterminate? In analysis (the theory behind calculus and beyond), limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits. However, if the expression obtained after this substitution does not provide sufficient information to determine the original limit, then the expression is called an indeterminate form. For example, we could say that $0/0$ is an indeterminate form.

But we need to more specific, this is still ambiguous. An indeterminate form is a mathematical expression involving at most two of $0$ , $1$ or $\infty$ , obtained by applying the algebraic limit theorem (a theorem in analysis, look this up for details) in the process of attempting to determine a limit, which fails to restrict that limit to one specific value or infinity, and thus does not determine the limit being calculated. This is why it is called indeterminate. Some examples of indeterminate forms are
$0/0, \infty/\infty, \infty-\infty, \infty \times 0$ etc etc. So what makes something undefined? In the broader scope, something being undefined refers to an expression which is not assigned an interpretation or a value. A function is said to be undefined for points outside its domain. For example, the function $f:\mathbb{R}^{+}\cup\{0\}\rightarrow\mathbb{R}$ given by the mapping $x\mapsto \sqrt{x}$ is undefined for $x<0$ . On the other hand, $1/0$ is undefined because dividing by $0$ is not defined in arithmetic by definition. In other words, something is undefined when it is not defined in some mathematical context.

Full post: A Letter to MSN

This post has been edited 1 time. Last edited by yummy-yum10-2021, Nov 11, 2024, 3:41 AM

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greenplanet2050

1303 posts

greenplanet2050

#25 h Nov 12, 2024, 11:43 PM

Y by

yummy-yum10-2021 wrote:

Arr0w wrote:

Greetings.

I have seen many posts talking about commonly asked questions, such as finding the value of $0^0$ , $\frac{1}{0}$ , $\frac{0}{0}$ , $\frac{\infty}{\infty}$ , why $0.999...=1$ or even expressions of those terms combined as if that would make them defined. I have made this post to answer these questions once and for all, and I politely ask everyone to link this post to threads that are talking about this issue.
[...]
What about $\frac{1}{0}$ ? Suppose that $x=\frac{1}{0}$ . Then we would have $x\cdot 0=0=1$ , absurd. A more rigorous treatment of the idea is that $\lim_{x\to0}\frac{1}{x}$ does not exist in the first place, although you will see why in a calculus course. So the point is that $\frac{1}{0}$ is undefined.
[...]
What about $\frac{0}{0}$ ? Usually this is considered to be an indeterminate form, but I would also wager that this is also undefined.
[...]
INDETERMINATE VS UNDEFINED

What makes something indeterminate? As you can see above, there are many things that are indeterminate. While definitions might vary slightly, it is the consensus that the following definition holds: A mathematical expression is be said to be indeterminate if it is not definitively or precisely determined. So how does this make, say, something like $0/0$ indeterminate? In analysis (the theory behind calculus and beyond), limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits. However, if the expression obtained after this substitution does not provide sufficient information to determine the original limit, then the expression is called an indeterminate form. For example, we could say that $0/0$ is an indeterminate form.

But we need to more specific, this is still ambiguous. An indeterminate form is a mathematical expression involving at most two of $0$ , $1$ or $\infty$ , obtained by applying the algebraic limit theorem (a theorem in analysis, look this up for details) in the process of attempting to determine a limit, which fails to restrict that limit to one specific value or infinity, and thus does not determine the limit being calculated. This is why it is called indeterminate. Some examples of indeterminate forms are
$0/0, \infty/\infty, \infty-\infty, \infty \times 0$ etc etc. So what makes something undefined? In the broader scope, something being undefined refers to an expression which is not assigned an interpretation or a value. A function is said to be undefined for points outside its domain. For example, the function $f:\mathbb{R}^{+}\cup\{0\}\rightarrow\mathbb{R}$ given by the mapping $x\mapsto \sqrt{x}$ is undefined for $x<0$ . On the other hand, $1/0$ is undefined because dividing by $0$ is not defined in arithmetic by definition. In other words, something is undefined when it is not defined in some mathematical context.

Full post: A Letter to MSN

There’s no need to bump this thread.

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vincentwant

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vincentwant

#26 h Nov 12, 2024, 11:47 PM

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me when the person who posted this is the same person who posted a letter to msm:

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Turtle09

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Turtle09

#27 h Nov 13, 2024, 12:25 AM

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vincentwant wrote:

me when the person who posted this is the same person who posted a letter to msm:

this is crazy lol

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sadas123

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sadas123

#28 h Nov 13, 2024, 1:49 AM

Y by

honestly I think that 1/0 is infinity because if you graph this on a graphing calculator it looks like this and you can see the largest red line is when you divide with 0 and if you do it with a smaller number with 1 which I will also include makes it a very large slope change, which looks like it is going to infinity.

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club52

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club52

#29 h Nov 13, 2024, 10:19 PM

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@above it goes to both positive and negative infinity.

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b2025tyx

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b2025tyx

#30 h Nov 14, 2024, 12:29 AM

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Sol 4

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blimpo

801 posts

blimpo

#31 h Nov 14, 2024, 4:34 AM

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I would like to point out that undefined and infinity are not numbers, but definitions. So you can't say "x is equal to infinity" or "when dividing this by undefined"

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