Divison by Zero [duplicate]
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This question already has an answer here:
Why not to extend the set of natural numbers to make it closed under division by zero?
6 answers
I have seen multiple answers on the web, but I can't get my mind around why division by zero outputs an error and not zero. Can anyone explain this in laymen's terms?
divisibility
asked Nov 15 at 18:46
Cody Rutscher
13
marked as duplicate by Community♦ Nov 15 at 19:07
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
up vote
-2
down vote
favorite
This question already has an answer here:
Why not to extend the set of natural numbers to make it closed under division by zero?
6 answers
I have seen multiple answers on the web, but I can't get my mind around why division by zero outputs an error and not zero. Can anyone explain this in laymen's terms?
divisibility
asked Nov 15 at 18:46
Cody Rutscher
13
marked as duplicate by Community♦ Nov 15 at 19:07
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
4
I bet this is a duplicate.
– vrugtehagel
Nov 15 at 18:48
On that note, see this post, this one, another one and one more
– vrugtehagel
Nov 15 at 18:51
@Cody Rutscher Basically, without going into all of the details, division by zero doesn't make sense. It is a question that doesn't have an answer. What is the color of the wind? Undefined.
– Prototank
Nov 15 at 19:00
Why on earth would it be $0$??? If $frac ab = x$ then that means by definition that $bx = a$. So if $frac 50 = x$ would mean by definition that $0*x = 5$. If $x = 0$ you get $0*0 = 5$ which is not true so $frac 50 ne 0$. You'll have to try something else. If $0*x = 5$ what is $x$. If you can answer that you are done. Can you answer that.
– fleablood
Nov 15 at 19:03
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
This question already has an answer here:
Why not to extend the set of natural numbers to make it closed under division by zero?
6 answers
I have seen multiple answers on the web, but I can't get my mind around why division by zero outputs an error and not zero. Can anyone explain this in laymen's terms?
divisibility
asked Nov 15 at 18:46
Cody Rutscher
13
This question already has an answer here:
Why not to extend the set of natural numbers to make it closed under division by zero?
6 answers
I have seen multiple answers on the web, but I can't get my mind around why division by zero outputs an error and not zero. Can anyone explain this in laymen's terms?
This question already has an answer here:
Why not to extend the set of natural numbers to make it closed under division by zero?
6 answers
divisibility
divisibility
asked Nov 15 at 18:46
Cody Rutscher
13
asked Nov 15 at 18:46
Cody Rutscher
13
asked Nov 15 at 18:46
Cody Rutscher
13
asked Nov 15 at 18:46
Cody Rutscher
13
asked Nov 15 at 18:46
Cody Rutscher
13
13
marked as duplicate by Community♦ Nov 15 at 19:07
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Community♦ Nov 15 at 19:07
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
4
I bet this is a duplicate.
– vrugtehagel
Nov 15 at 18:48
On that note, see this post, this one, another one and one more
– vrugtehagel
Nov 15 at 18:51
@Cody Rutscher Basically, without going into all of the details, division by zero doesn't make sense. It is a question that doesn't have an answer. What is the color of the wind? Undefined.
– Prototank
Nov 15 at 19:00
Why on earth would it be $0$??? If $frac ab = x$ then that means by definition that $bx = a$. So if $frac 50 = x$ would mean by definition that $0*x = 5$. If $x = 0$ you get $0*0 = 5$ which is not true so $frac 50 ne 0$. You'll have to try something else. If $0*x = 5$ what is $x$. If you can answer that you are done. Can you answer that.
– fleablood
Nov 15 at 19:03
add a comment |
4
I bet this is a duplicate.
– vrugtehagel
Nov 15 at 18:48
On that note, see this post, this one, another one and one more
– vrugtehagel
Nov 15 at 18:51
@Cody Rutscher Basically, without going into all of the details, division by zero doesn't make sense. It is a question that doesn't have an answer. What is the color of the wind? Undefined.
– Prototank
Nov 15 at 19:00
Why on earth would it be $0$??? If $frac ab = x$ then that means by definition that $bx = a$. So if $frac 50 = x$ would mean by definition that $0*x = 5$. If $x = 0$ you get $0*0 = 5$ which is not true so $frac 50 ne 0$. You'll have to try something else. If $0*x = 5$ what is $x$. If you can answer that you are done. Can you answer that.
– fleablood
Nov 15 at 19:03
4
4
I bet this is a duplicate.
– vrugtehagel
Nov 15 at 18:48
I bet this is a duplicate.
– vrugtehagel
Nov 15 at 18:48
On that note, see this post, this one, another one and one more
– vrugtehagel
Nov 15 at 18:51
On that note, see this post, this one, another one and one more
– vrugtehagel
Nov 15 at 18:51
@Cody Rutscher Basically, without going into all of the details, division by zero doesn't make sense. It is a question that doesn't have an answer. What is the color of the wind? Undefined.
– Prototank
Nov 15 at 19:00
@Cody Rutscher Basically, without going into all of the details, division by zero doesn't make sense. It is a question that doesn't have an answer. What is the color of the wind? Undefined.
– Prototank
Nov 15 at 19:00
Why on earth would it be $0$??? If $frac ab = x$ then that means by definition that $bx = a$. So if $frac 50 = x$ would mean by definition that $0*x = 5$. If $x = 0$ you get $0*0 = 5$ which is not true so $frac 50 ne 0$. You'll have to try something else. If $0*x = 5$ what is $x$. If you can answer that you are done. Can you answer that.
– fleablood
Nov 15 at 19:03
Why on earth would it be $0$??? If $frac ab = x$ then that means by definition that $bx = a$. So if $frac 50 = x$ would mean by definition that $0*x = 5$. If $x = 0$ you get $0*0 = 5$ which is not true so $frac 50 ne 0$. You'll have to try something else. If $0*x = 5$ what is $x$. If you can answer that you are done. Can you answer that.
– fleablood
Nov 15 at 19:03
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Well, let's try it. Let's divide $x$ by $0$ and say it's equal to some number $y$. Then
$$frac x0=y.$$
By definition, we may multiply both sides by $0$, and see $x=ycdot0=0$. This isn't true; we didn't assume $x$ to be zero. However, this tells us the only number we can divide by $0$ is $0$ itself; indeed, $tfrac00=y$ doesn't result in a contradiction.
The problem with saying $tfrac00$ is defined, is that it is everything at once. It doesn't have only one value. $tfrac00=1$ wouldn't reach a contradiction (not by multiplying by $0$, that is) and neither would $tfrac00=0$. In mathematics, we like things to only represent one thing and one thing only. If we would let $tfrac00$ mean both $0$ and $1$ at the same time, then we wouldn't be able to use $=$ like we want; if we did, then
$$0=frac00=1implies 0=1$$
So, that would be a hassle for just letting this thing that is everything at once exist. Hence, we just agree to not divide by $0$, so we can keep all our rules, axioms, and theorems we know.
answered Nov 15 at 18:58
vrugtehagel
10.7k1549
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Well, let's try it. Let's divide $x$ by $0$ and say it's equal to some number $y$. Then
$$frac x0=y.$$
By definition, we may multiply both sides by $0$, and see $x=ycdot0=0$. This isn't true; we didn't assume $x$ to be zero. However, this tells us the only number we can divide by $0$ is $0$ itself; indeed, $tfrac00=y$ doesn't result in a contradiction.
The problem with saying $tfrac00$ is defined, is that it is everything at once. It doesn't have only one value. $tfrac00=1$ wouldn't reach a contradiction (not by multiplying by $0$, that is) and neither would $tfrac00=0$. In mathematics, we like things to only represent one thing and one thing only. If we would let $tfrac00$ mean both $0$ and $1$ at the same time, then we wouldn't be able to use $=$ like we want; if we did, then
$$0=frac00=1implies 0=1$$
So, that would be a hassle for just letting this thing that is everything at once exist. Hence, we just agree to not divide by $0$, so we can keep all our rules, axioms, and theorems we know.
answered Nov 15 at 18:58
vrugtehagel
10.7k1549
add a comment |
up vote
1
down vote
accepted
Well, let's try it. Let's divide $x$ by $0$ and say it's equal to some number $y$. Then
$$frac x0=y.$$
By definition, we may multiply both sides by $0$, and see $x=ycdot0=0$. This isn't true; we didn't assume $x$ to be zero. However, this tells us the only number we can divide by $0$ is $0$ itself; indeed, $tfrac00=y$ doesn't result in a contradiction.
The problem with saying $tfrac00$ is defined, is that it is everything at once. It doesn't have only one value. $tfrac00=1$ wouldn't reach a contradiction (not by multiplying by $0$, that is) and neither would $tfrac00=0$. In mathematics, we like things to only represent one thing and one thing only. If we would let $tfrac00$ mean both $0$ and $1$ at the same time, then we wouldn't be able to use $=$ like we want; if we did, then
$$0=frac00=1implies 0=1$$
So, that would be a hassle for just letting this thing that is everything at once exist. Hence, we just agree to not divide by $0$, so we can keep all our rules, axioms, and theorems we know.
answered Nov 15 at 18:58
vrugtehagel
10.7k1549
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Well, let's try it. Let's divide $x$ by $0$ and say it's equal to some number $y$. Then
$$frac x0=y.$$
By definition, we may multiply both sides by $0$, and see $x=ycdot0=0$. This isn't true; we didn't assume $x$ to be zero. However, this tells us the only number we can divide by $0$ is $0$ itself; indeed, $tfrac00=y$ doesn't result in a contradiction.
The problem with saying $tfrac00$ is defined, is that it is everything at once. It doesn't have only one value. $tfrac00=1$ wouldn't reach a contradiction (not by multiplying by $0$, that is) and neither would $tfrac00=0$. In mathematics, we like things to only represent one thing and one thing only. If we would let $tfrac00$ mean both $0$ and $1$ at the same time, then we wouldn't be able to use $=$ like we want; if we did, then
$$0=frac00=1implies 0=1$$
So, that would be a hassle for just letting this thing that is everything at once exist. Hence, we just agree to not divide by $0$, so we can keep all our rules, axioms, and theorems we know.
answered Nov 15 at 18:58
vrugtehagel
10.7k1549
Well, let's try it. Let's divide $x$ by $0$ and say it's equal to some number $y$. Then
$$frac x0=y.$$
By definition, we may multiply both sides by $0$, and see $x=ycdot0=0$. This isn't true; we didn't assume $x$ to be zero. However, this tells us the only number we can divide by $0$ is $0$ itself; indeed, $tfrac00=y$ doesn't result in a contradiction.
The problem with saying $tfrac00$ is defined, is that it is everything at once. It doesn't have only one value. $tfrac00=1$ wouldn't reach a contradiction (not by multiplying by $0$, that is) and neither would $tfrac00=0$. In mathematics, we like things to only represent one thing and one thing only. If we would let $tfrac00$ mean both $0$ and $1$ at the same time, then we wouldn't be able to use $=$ like we want; if we did, then
$$0=frac00=1implies 0=1$$
So, that would be a hassle for just letting this thing that is everything at once exist. Hence, we just agree to not divide by $0$, so we can keep all our rules, axioms, and theorems we know.
answered Nov 15 at 18:58
vrugtehagel
10.7k1549
answered Nov 15 at 18:58
vrugtehagel
10.7k1549
answered Nov 15 at 18:58
vrugtehagel
10.7k1549
answered Nov 15 at 18:58
vrugtehagel
10.7k1549
10.7k1549
add a comment |
add a comment |
4
I bet this is a duplicate.
– vrugtehagel
Nov 15 at 18:48
On that note, see this post, this one, another one and one more
– vrugtehagel
Nov 15 at 18:51
@Cody Rutscher Basically, without going into all of the details, division by zero doesn't make sense. It is a question that doesn't have an answer. What is the color of the wind? Undefined.
– Prototank
Nov 15 at 19:00
Why on earth would it be $0$??? If $frac ab = x$ then that means by definition that $bx = a$. So if $frac 50 = x$ would mean by definition that $0*x = 5$. If $x = 0$ you get $0*0 = 5$ which is not true so $frac 50 ne 0$. You'll have to try something else. If $0*x = 5$ what is $x$. If you can answer that you are done. Can you answer that.
– fleablood
Nov 15 at 19:03