The Reason For The Proscription Against Division By Zero

This IS a TEST; Do you know the ACTUAL reason division by zero is not permitted?

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The Reason For The Proscription Against Division By Zero

#1  Postby scherado » Oct 25, 2018 10:06 pm

All-righty then. This thread will separate the "men from the boys," this expression having been created, I suppose, when women were second-class citizens; but that's water under the bridge and not the topic.

If you do a search for the answer, then you provide your reference and it can't be wookee-peee-D-uh.

You learned this in grade-school, one may presume, were reminded of it in high school and taught the exact reason for it in college/university, if you took any college-level Mathematics, though I don't remember the exact class in which I learned this, possibly The Calculus.

I will add that my professor did not express the answer in the words I will, eventually.

The question: What's the reason we can't divide by zero?

We were told "it's undefined." That doesn't tell us much. When I ask this question to people who damn well should know I have been shocked, repeatedly.
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Re: The Reason For The Proscription Against Division By Zero

#2  Postby Thomas Eshuis » Oct 25, 2018 10:08 pm

Oh look, more vapid trolling. :roll:
"Respect for personal beliefs = "I am going to tell you all what I think of YOU, but don't dare retort and tell what you think of ME because...it's my personal belief". Hmm. A bully's charter and no mistake."
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Re: The Reason For The Proscription Against Division By Zero

#3  Postby scherado » Oct 25, 2018 10:09 pm

ROTFLMAO!!!!!!

We've got someone who thinks he knows, but....does he???? We may never know...
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Re: The Reason For The Proscription Against Division By Zero

#4  Postby Thomas Eshuis » Oct 25, 2018 10:16 pm

scherado wrote:ROTFLMAO!!!!!!

We've got someone who thinks he knows, but....does he???? We may never know...

We've got someone who thinks he can troll, but he can't. :roll:
"Respect for personal beliefs = "I am going to tell you all what I think of YOU, but don't dare retort and tell what you think of ME because...it's my personal belief". Hmm. A bully's charter and no mistake."
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Re: The Reason For The Proscription Against Division By Zero

#5  Postby Thommo » Oct 25, 2018 10:19 pm

Posted within the last hour:
scherado wrote:I don't pretend to be a teacher.


:lol:

Anyway, the real numbers are defined to be a field (the unique complete Archimedean field), which requires that under addition and multiplication they are closed, associative, have inverses and have a null element wherever those operations are defined. Multiplication by zero does not have an inverse and cannot sensibly be given one (on that set and structure) and thus is not defined on that field.

No, this is not how it is explained in grade school.

Anyway, you can learn lots about this at this perfectly acceptable and excellent link:
https://en.wikipedia.org/wiki/Division_by_zero

Edit: Corrected miswriting of "multiplication" as "division".
Last edited by Thommo on Oct 25, 2018 11:27 pm, edited 3 times in total.
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Re: The Reason For The Proscription Against Division By Zero

#6  Postby laklak » Oct 25, 2018 10:20 pm

:coffee:
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The sky is falling! The sky is falling! - Chicken Little
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Re: The Reason For The Proscription Against Division By Zero

#7  Postby BlackBart » Oct 25, 2018 10:32 pm

Dividing a number by zero is the same as not dividing it by anything therefore...

A/0 = A

A/1 also equals A

Therefore 1 is equal to 0

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Re: The Reason For The Proscription Against Division By Zero

#8  Postby Thommo » Oct 25, 2018 10:41 pm

BlackBart wrote:Dividing a number by zero is the same as not dividing it by anything therefore...

A/0 = A

A/1 also equals A

Therefore 1 is equal to 0

Take that atheists!!


Zero ring!
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Re: The Reason For The Proscription Against Division By Zero

#9  Postby scherado » Oct 25, 2018 11:01 pm

Thommo wrote:Posted within the last hour:
scherado wrote:I don't pretend to be a teacher.


:lol:

Anyway, the real numbers are defined to be a field (the unique complete Archimedean field), which requires that under addition and multiplication they are closed, associative, have inverses and have a null element wherever those operations are defined. Division by zero does not have an inverse and cannot sensibly be given one (on that set and structure) and thus is not defined on that field.

No, this is not how it is explained in grade school.

Anyway, you can learn lots about this at this perfectly acceptable and excellent link:
https://en.wikipedia.org/wiki/Division_by_zero

Nope, no Whiiikee-peee-D-uh references.

Come on! Don't you think you've got the cart before the horse with: Division by zero does not have an inverse and cannot sensibly be given one.

Division by zero can not be done never mind considering an inverse.

This is going to be fun; and I KNOW that you know that I'm NOT whittling Dixie!
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Re: The Reason For The Proscription Against Division By Zero

#10  Postby Matt_B » Oct 25, 2018 11:17 pm

You're getting it all wrong. This has to be answered entirely with conservative rhetoric:

1. It's political correctness gone mad.
2. It's against first amendment rights.
3. It says so in the Bible, right there next to the bit where Pi is defined as 3.
4. It'd send the budget deficit up towards infinity, if you could.
5. It says Error on my calculator just to hide the Truth.
6. Make mathematics great again.
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Re: The Reason For The Proscription Against Division By Zero

#11  Postby Thommo » Oct 25, 2018 11:26 pm

scherado wrote:
Thommo wrote:Posted within the last hour:
scherado wrote:I don't pretend to be a teacher.


:lol:

Anyway, the real numbers are defined to be a field (the unique complete Archimedean field), which requires that under addition and multiplication they are closed, associative, have inverses and have a null element wherever those operations are defined. Division by zero does not have an inverse and cannot sensibly be given one (on that set and structure) and thus is not defined on that field.

No, this is not how it is explained in grade school.

Anyway, you can learn lots about this at this perfectly acceptable and excellent link:
https://en.wikipedia.org/wiki/Division_by_zero

Nope, no Whiiikee-peee-D-uh references.


There clearly was one. You can complain all you want, you're impotent to prevent it being linked.

It's likely to be more thorough and accurate than answers anyone here can provide at short notice.

scherado wrote:Come on! Don't you think you've got the cart before the horse with: Division by zero does not have an inverse and cannot sensibly be given one.


Yeah, I meant "multiplication". That's a mistake. I'll edit in the correction.

The clause should read "Multiplication by zero does not have an inverse and cannot sensibly be given one".
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Re: The Reason For The Proscription Against Division By Zero

#12  Postby Spinozasgalt » Oct 26, 2018 12:05 am

scherado wrote:All-righty then. This thread will separate the "men from the boys," this expression having been created, I suppose, when women were second-class citizens; but that's water under the bridge and not the topic.

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Re: The Reason For The Proscription Against Division By Zero

#13  Postby scherado » Oct 26, 2018 12:14 am

Matt_B wrote:You're getting it all wrong. This has to be answered entirely with conservative rhetoric:

1. It's political correctness gone mad.
2. It's against first amendment rights.
3. It says so in the Bible, right there next to the bit where Pi is defined as 3.
4. It'd send the budget deficit up towards infinity, if you could.
5. It says Error on my calculator just to hide the Truth.
6. Make mathematics great again.

Matt...unhinged.
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Re: The Reason For The Proscription Against Division By Zero

#14  Postby scherado » Oct 26, 2018 12:19 am

Thommo wrote:..The clause should read "Multiplication by zero does not have an inverse and cannot sensibly be given one".

I think you want to start your own thread: The Reason For The Proscription Against Multiplication By Zero[/i]. Good luck to you.
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Re: The Reason For The Proscription Against Division By Zero

#15  Postby Thommo » Oct 26, 2018 12:29 am

scherado wrote:
Thommo wrote:...The clause should read "Multiplication by zero does not have an inverse and cannot sensibly be given one".

I think you want to start your own thread: The Reason For The Proscription Against Multiplication By Zero. Good luck to you.


Err, no. That is a correct answer to the thread title.

There is no prescription against multiplication by zero.
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Re: The Reason For The Proscription Against Division By Zero

#16  Postby The_Metatron » Oct 26, 2018 1:10 am

Eddie Woo addresses this in nine minutes on the youtubes.
I AM Skepdickus!

Check out Hack's blog, too. He writes good.
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Re: The Reason For The Proscription Against Division By Zero

#17  Postby Thommo » Oct 26, 2018 1:48 am

Start from the field axioms:
https://en.wikipedia.org/wiki/Field_(mathematics)#Classic_definition
Classic definition

Formally, a field is a set F together with two operations called addition and multiplication.[1] An operation is a mapping that associates an element of the set to every pair of its elements. The result of the addition of a and b is called the sum of a and b and denoted a + b. Similarly, the result of the multiplication of a and b is called the product of a and b, and denoted ab or a⋅b. These operations are required to satisfy the following properties, referred to as field axioms. In the following definitions, a, b and c are arbitrary elements of the field F.

Associativity of addition and multiplication: a + (b + c) = (a + b) + c and a · (b · c) = (a · b) · c.
Commutativity of addition and multiplication: a + b = b + a and a · b = b · a.
Additive and multiplicative identity: there exist two different elements 0 and 1 in F such that a + 0 = a and a · 1 = a.
Additive inverses: for every a in F, there exists an element in F, denoted −a, called additive inverse of a, such that a + (−a) = 0.
Multiplicative inverses: for every a ≠ 0 in F, there exists an element in F, denoted by a−1, 1/a, or 1/a, called the multiplicative inverse of a, such that a · a−1 = 1.
Distributivity of multiplication over addition: a · (b + c) = (a · b) + (a · c).

This may be summarized by saying: a field has two operations, called addition and multiplication; it is an abelian group under the addition, with 0 as additive identity; the nonzero elements are an abelian group under the multiplication, with 1 as multiplicative identity; the multiplication is distributive over the addition.


Prove 0.a = 0 for any a:
b + 0 = b [by definition of 0, for any b]
∴ 0 + b = b [by commutativity of addition]
∴ 0 + 1 = 1
Multiply both sides by a:
a*(0 + 1) = a*1
∴ a*0 + a*1 = a*1 [by distributive law]
∴ a*0 + a = a [by definition of 1]
Add -a to both sides:
(a*0 + a) + (-a) = a + (-a)
∴ a*0 + (a + (-a)) = a + (-a) [by associative property of addition]
∴ a*0 + 0 = 0 [by definition of additive inverse]
∴ a*0 = 0 [by definition of additive identity]

QED.

Then observe that if we define a new structure, which has an element 0-1 such that 00-1 = 1 then by the previous result 0 = 1 and hence a*0 = a*1, which reduces to 0 = a for any a. Which means we have the zero ring and not a field.

Therefore if we want to have an inverse for 0 we have to give up on some of the field axioms (which by definition are axioms of the reals).
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Re: The Reason For The Proscription Against Division By Zero

#18  Postby Matt_B » Oct 26, 2018 4:01 am

scherado wrote:
Matt_B wrote:You're getting it all wrong. This has to be answered entirely with conservative rhetoric:

1. It's political correctness gone mad.
2. It's against first amendment rights.
3. It says so in the Bible, right there next to the bit where Pi is defined as 3.
4. It'd send the budget deficit up towards infinity, if you could.
5. It says Error on my calculator just to hide the Truth.
6. Make mathematics great again.

Matt...unhinged.


That's the effect I was going for. I hope you'll have the same reaction whenever you see the same devices employed in political discussions too. :lol:

Anyway, my serious answer would be that there's no such proscription if you look at advanced enough mathematics. For instance, 1/0 leads to a well defined point on the Riemann sphere, albeit under a different definition of division that you can't naively translate back to real algebra.

One thing I'm sure we can all agree upon is that the result of 1/0 could not be a real number. Thommo has outlined one reason why, but more intuitively you could just take the limit of 1/x as x tends to 0 from above and below, and you'll see it shooting off towards infinity in both directions. Infinities are not real numbers, therefore it's sensible to leave the result undefined in any areas of mathematics where we're looking for a real result.
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Re: The Reason For The Proscription Against Division By Zero

#19  Postby Cito di Pense » Oct 26, 2018 7:31 am

scherado wrote:If you do a search for the answer, then you provide your reference and it can't be wookee-peee-D-uh.


http://mathworld.wolfram.com/DivisionbyZero.html

There ya go. Non-Wikipedia reference provided, backing up Thommo's and MattB's points. It comes complete with links and footnotes that will permit you to educate yourself further, taking your genius to the next level.

scherado wrote:Division by zero can not be done never mind considering an inverse.


For your next trick, I suggest complaining about how .9999... is not 1 in the set of real numbers.

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Re: The Reason For The Proscription Against Division By Zero

#20  Postby Evolving » Oct 26, 2018 9:07 am

Cito di Pense wrote:
For your next trick, I suggest complaining about how .9999... is not 1 in the set of real numbers.


oh god, not that again, please!
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