Tjyylli

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Another proof that dividing by 0 does not exist — is it right?

13

2

$begingroup$

Ok I am in grade 9 and I am maybe too young for this.

But I thought about this, why dividing by 0 is impossible.

Dividing by 0 is possible would mean 1/0 is possible, which would mean 0 has a multiplicative inverse.

So if we multiply a number by 0 then by 1/0 we get the same number.

But thats impossible because all numbers multiplied by 0 gives 0 therefore we can’t have an inverse for 0, as that gives us the initial number and thus division by 0 is impossible

Is this right?

proof-verification

share|cite|improve this question

edited 9 mins ago

H Huang

401111

asked 5 hours ago

Selim Jean ElliehSelim Jean Ellieh

764

New contributor

Selim Jean Ellieh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sometimes division by zero is defined, such as in the extended complex plane.
  $endgroup$
  – Shaun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  $begingroup$
  Your answer is 100% correct and you should probably become a mathematician. These kinds of answers (mathematicians also call them proofs) are what mathematicians do all day long.
  $endgroup$
  – ErotemeObelus
  1 hour ago
  
  
  

  
  
  
  

add a comment | 

13

2

$begingroup$

Ok I am in grade 9 and I am maybe too young for this.

But I thought about this, why dividing by 0 is impossible.

Dividing by 0 is possible would mean 1/0 is possible, which would mean 0 has a multiplicative inverse.

So if we multiply a number by 0 then by 1/0 we get the same number.

But thats impossible because all numbers multiplied by 0 gives 0 therefore we can’t have an inverse for 0, as that gives us the initial number and thus division by 0 is impossible

Is this right?

proof-verification

share|cite|improve this question

edited 9 mins ago

H Huang

401111

asked 5 hours ago

Selim Jean ElliehSelim Jean Ellieh

764

New contributor

Selim Jean Ellieh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sometimes division by zero is defined, such as in the extended complex plane.
  $endgroup$
  – Shaun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  $begingroup$
  Your answer is 100% correct and you should probably become a mathematician. These kinds of answers (mathematicians also call them proofs) are what mathematicians do all day long.
  $endgroup$
  – ErotemeObelus
  1 hour ago
  
  
  

  
  
  
  

add a comment | 

$begingroup$

Ok I am in grade 9 and I am maybe too young for this.

But I thought about this, why dividing by 0 is impossible.

Dividing by 0 is possible would mean 1/0 is possible, which would mean 0 has a multiplicative inverse.

So if we multiply a number by 0 then by 1/0 we get the same number.

But thats impossible because all numbers multiplied by 0 gives 0 therefore we can’t have an inverse for 0, as that gives us the initial number and thus division by 0 is impossible

Is this right?

proof-verification

share|cite|improve this question

edited 9 mins ago

H Huang

401111

asked 5 hours ago

Selim Jean ElliehSelim Jean Ellieh

764

New contributor

Selim Jean Ellieh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited 9 mins ago

H Huang

401111

asked 5 hours ago

Selim Jean ElliehSelim Jean Ellieh

764

New contributor

Selim Jean Ellieh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited 9 mins ago

H Huang

401111

asked 5 hours ago

Selim Jean ElliehSelim Jean Ellieh

764

New contributor

Selim Jean Ellieh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited 9 mins ago

H Huang

401111

edited 9 mins ago

H Huang

401111

asked 5 hours ago

Selim Jean ElliehSelim Jean Ellieh

764

New contributor

Selim Jean Ellieh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 5 hours ago

Selim Jean ElliehSelim Jean Ellieh

764

2 Answers
2

active

oldest

votes

18

$begingroup$

That's the most basic reason that division by $0$ is usually considered to be a Bad Thing, yes. Because if we did allow dividing by $0$, we would have to give up at least of one of the following things (these are usually considered Very Nice):

• What $1$ means ($1cdot a = a$ for any $a$)


• What $0$ means ($0 cdot a = 0$ for any $a$)


• What division means ($frac ab = c$ means $a = ccdot b$)

share|cite|improve this answer

answered 5 hours ago

ArthurArthur

121k7121208

$endgroup$

add a comment | 

5

$begingroup$

Yes . . . and no.

You might be interested in, for example, Wheel Theory, where division by zero is defined.

share|cite|improve this answer

edited 5 hours ago

answered 5 hours ago

ShaunShaun

9,923113684

$endgroup$

• 
  
  
  

  
  9
  

  
  
  
  
  
  

  
  $begingroup$
  You think this is very relevant for a ninth grader? I mean, it might be cool to know it's out there, but does this really answer the question that is asked?
  $endgroup$
  – Arthur
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  That's a fair comment, @Arthur. Thank you for the feedback.
  $endgroup$
  – Shaun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What d'you think, @SelimJeanEllieh?
  $endgroup$
  – Shaun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Oh: The OP has insufficient rep to comment. Nevermind.
  $endgroup$
  – Shaun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  $begingroup$
  @Arthur I think this is extremely relevant. It shows that division by zero isn't some sort of sacred thing that we must not touch, it's just contradictory to the three Very Nice things in your post, and there are systems of "multiplication" and "division" out there where we are allowed to divide by zero. +1 for this answer.
  $endgroup$
  – YiFan
  2 hours ago
  

  
  
  
  

 | 
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18

$begingroup$

That's the most basic reason that division by $0$ is usually considered to be a Bad Thing, yes. Because if we did allow dividing by $0$, we would have to give up at least of one of the following things (these are usually considered Very Nice):

• What $1$ means ($1cdot a = a$ for any $a$)


• What $0$ means ($0 cdot a = 0$ for any $a$)


• What division means ($frac ab = c$ means $a = ccdot b$)

share|cite|improve this answer

answered 5 hours ago

ArthurArthur

121k7121208

$endgroup$

add a comment | 

18

$begingroup$

That's the most basic reason that division by $0$ is usually considered to be a Bad Thing, yes. Because if we did allow dividing by $0$, we would have to give up at least of one of the following things (these are usually considered Very Nice):

• What $1$ means ($1cdot a = a$ for any $a$)


• What $0$ means ($0 cdot a = 0$ for any $a$)


• What division means ($frac ab = c$ means $a = ccdot b$)

share|cite|improve this answer

answered 5 hours ago

ArthurArthur

121k7121208

$endgroup$

add a comment | 

$begingroup$

That's the most basic reason that division by $0$ is usually considered to be a Bad Thing, yes. Because if we did allow dividing by $0$, we would have to give up at least of one of the following things (these are usually considered Very Nice):

• What $1$ means ($1cdot a = a$ for any $a$)


• What $0$ means ($0 cdot a = 0$ for any $a$)


• What division means ($frac ab = c$ means $a = ccdot b$)

share|cite|improve this answer

answered 5 hours ago

ArthurArthur

121k7121208

$endgroup$

share|cite|improve this answer

answered 5 hours ago

ArthurArthur

121k7121208

answered 5 hours ago

ArthurArthur

121k7121208

answered 5 hours ago

ArthurArthur

121k7121208

5

$begingroup$

Yes . . . and no.

You might be interested in, for example, Wheel Theory, where division by zero is defined.

share|cite|improve this answer

edited 5 hours ago

answered 5 hours ago

ShaunShaun

9,923113684

$endgroup$

• 
  
  
  

  
  9
  

  
  
  
  
  
  

  
  $begingroup$
  You think this is very relevant for a ninth grader? I mean, it might be cool to know it's out there, but does this really answer the question that is asked?
  $endgroup$
  – Arthur
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  That's a fair comment, @Arthur. Thank you for the feedback.
  $endgroup$
  – Shaun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What d'you think, @SelimJeanEllieh?
  $endgroup$
  – Shaun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Oh: The OP has insufficient rep to comment. Nevermind.
  $endgroup$
  – Shaun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  $begingroup$
  @Arthur I think this is extremely relevant. It shows that division by zero isn't some sort of sacred thing that we must not touch, it's just contradictory to the three Very Nice things in your post, and there are systems of "multiplication" and "division" out there where we are allowed to divide by zero. +1 for this answer.
  $endgroup$
  – YiFan
  2 hours ago
  

  
  
  
  

 | 
show 1 more comment

5

$begingroup$

Yes . . . and no.

You might be interested in, for example, Wheel Theory, where division by zero is defined.

share|cite|improve this answer

edited 5 hours ago

answered 5 hours ago

ShaunShaun

9,923113684

$endgroup$

• 
  
  
  

  
  9
  

  
  
  
  
  
  

  
  $begingroup$
  You think this is very relevant for a ninth grader? I mean, it might be cool to know it's out there, but does this really answer the question that is asked?
  $endgroup$
  – Arthur
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  That's a fair comment, @Arthur. Thank you for the feedback.
  $endgroup$
  – Shaun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What d'you think, @SelimJeanEllieh?
  $endgroup$
  – Shaun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Oh: The OP has insufficient rep to comment. Nevermind.
  $endgroup$
  – Shaun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  $begingroup$
  @Arthur I think this is extremely relevant. It shows that division by zero isn't some sort of sacred thing that we must not touch, it's just contradictory to the three Very Nice things in your post, and there are systems of "multiplication" and "division" out there where we are allowed to divide by zero. +1 for this answer.
  $endgroup$
  – YiFan
  2 hours ago
  

  
  
  
  

 | 
show 1 more comment

$begingroup$

Yes . . . and no.

You might be interested in, for example, Wheel Theory, where division by zero is defined.

share|cite|improve this answer

edited 5 hours ago

answered 5 hours ago

ShaunShaun

9,923113684

$endgroup$

share|cite|improve this answer

edited 5 hours ago

answered 5 hours ago

ShaunShaun

9,923113684

answered 5 hours ago

ShaunShaun

9,923113684

answered 5 hours ago

ShaunShaun

9,923113684