# 0÷0

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If 50÷1 is 50 so 1 fits 50 times so

I need to ask you how many times does 0 fit in 0 0 times right? So 0÷0=0?

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Wrong, unfortunately. 0 divided by 0 is undefined. Why? you might ask? The rule in math is that anything divided by itself is 1. This would argue that 0/0=1. However, zero has peculiar properties that prevent this. For example, 16/16 = 1, but 16 = 4 x 4, so 16/16 is the same as 4x4/4x4. but 4/4 = 1, so 4x4/4x4 = 1 x 1 = 1, and 16/16 = 1. The point of this example is that if we divide a non-zero number by itself, we always get an answer of 1, even if we factor the number.

Now, consider 0/0. 50 x 0 = 0, and 1 x 0 = 0, so 0/0 could be 50x0/1x0. if 0/0=1, then this version of 0/0 = 50. The point here is that the answer changes depending on what numbers were multiplied to make zero. This, then, defeats mathematics, which is why the result you are seeking is "undefined" in mathematics.

Attempting to divide any number by zero, even zero itself, creates inconsistencies in mathematics, and is not permitted.

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^a good (and brief) explanation from good (and talented) explainers

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Let x = y

x^2 = x.y

x^2 - y^2 = x.y - y^2

(x + y)(x - y) = y(x - y)

cancel out the (x - y)

x + y = y

2 = 1

Spot the error, or accept that 2 = 1

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Let x = y

x^2 = x.y

x^2 - y^2 = x.y - y^2

(x + y)(x - y) = y(x - y)

cancel out the (x - y)

x + y = y

2 = 1

Spot the error, or accept that 2 = 1

canceling out (x-y) produces a divide by zero error

Edited by TakenItSeriously
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0/0, like any non-zero number divided by 0 does not equal any specific number so "does not exist".

However, some texts, particularly those such as Calculus texts, that deal with limits, distinguish between the "non-zero divided by 0" and "0 divided by 0" by calling the latter "undetermined" rather than undefined.

If it were true that a/0= b then a= b*0. If a is not 0, then there is no b that makes that true- it is "undefined". But if a= 0, that says 0= b*0 which is true for all b. There is no single value of b that we can assign to b.

If we had a problem say, $\lim_{x\to 2}\frac{x+ 3}{x- 2}$ by just putting x equal to 2 in $\frac{x+ 3}{x- 2}$ we get $\frac{5}{0}$ so we know immediately that the limit does not exist.
But if the problem were $\lim_{x\to 2}\frac{x^2- 4}{x- 2}$ then putting x equal to 2 we get $\frac{0}{0}$ so there might be a limit. We observe that, for any x other than 2, $\frac{x^2- 4}{x- 2}= \frac{(x-2)(x+ 2)}{x- 2}= x+ 2$ so the limit, as x goes to 2, is 2+ 2= 4.

Edited by Country Boy
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• 3 weeks later...

0/0 is undefined and that is why we evaluate such functions using limits.

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• 2 months later...

Yes to all that, but does anyone know the reason we can't divide by zero?

I give the answer in five words, no numbers. I will give my answer tomorrow.

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Yes to all that, but does anyone know the reason we can't divide by zero?

I give the answer in five words, no numbers. I will give my answer tomorrow.

Yes, I do. But please ignore me.

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Yes to all that, but does anyone know the reason we can't divide by zero?

I give the answer in five words, no numbers. I will give my answer tomorrow.

!

Moderator Note

This posting style/tactic gets really old, really fast. Discontinue your implementation of it, please.

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2 hours ago, swansont said:
!

Moderator Note

This posting style/tactic gets really old, really fast. Discontinue your implementation of it, please.

I will answer the question tonight. Thank you.

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Infinity is not a value.

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On 6/30/2017 at 8:15 PM, HallsofIvy said:

0/0, like any non-zero number divided by 0 does not equal any specific number so "does not exist".

However, some texts, particularly those such as Calculus texts, that deal with limits, distinguish between the "non-zero divided by 0" and "0 divided by 0" by calling the latter "undetermined" rather than undefined.

If it were true that a/0= ...

I don't understand the reason you proceed after the point at which I cut-off your If/Then: Infinity is not a value, therefore it can not "=" anything.

On 6/20/2017 at 7:45 PM, 0÷0is Easy said:

If 50÷1 is 50 so 1 fits 50 times so

I need to ask you how many times does 0 fit in 0 0 times right? So 0÷0=0?

I left out the part where zero is not a value.

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I don't understand the reason you proceed after the point at which I cut-off your If/Then: Infinity is not a value, therefore it can not "=" anything.

I left out the part where zero is not a value.

I think you have misunderstood what Halls of Ivy said.

Putting words he did not say into the quote does not help either.

He said that 0/0 is not a specific number.

He did not say that either infinity or zero are not numbers or values.

I will leave the issue of infinity aside since it is the more complicated of the two and off topic here.

I left out the part where zero is not a value.

Zero on the other hand is most decidedly a perfectly respectable number.

Failure to recognise this held back Mathematics for several thousand years.

Let us examine the situation more closely.

For most of its history mathematics was developed by practical persons needing figures to carry out their daily life.
Also throughout history these processes were isolated from the praticality and formalised into the discipline we know call Mathematics.

So we start where the ancients started. With arithmetic.
They identified four processes as forming a vital basis for arithmetic, long before algebra was invented.

These are addition, subtraction, multiplication and division and I am going to use the modern description for these.

I will come back and finish this.

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11 minutes ago, studiot said:

I think you have misunderstood what Halls of Ivy said.

Putting words he did not say into the quote does not help either.

He said that 0/0 is not a specific number.

He did not say that either infinity or zero are not numbers or values.

I will leave the issue of infinity aside since it is the more complicated of the two and off topic here.

...

It is exactly the reason one can't divide by zero. Are you using some personal definitions of "off" "topic" and "here"?

The illustration of inability to divide by zero is made by watching the value of a fraction when it's denominator decreases repeatedly.

3/1 = 3
3/.5 = 6
3/.25 = 12
3/.1 = 30
3/.01 = 300

One could reduce the denominator forever, approaching zero but never reaching zero. Putting the numbers to a graph X,Y the axis would extend forever and the graph can't be completed....which brings us to the "concept" of infinite distance, but we are discussing mathematical (numerical) infinity.

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Infinity is not a value.

Well, praise is due for a sentence which is simple, clear, grammatically correct and factually correct. I might have given you an upvote, but for the fact it is also largely irrelevant.

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Why couldn't you wait till I came back and finished my post as I promised?

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It is exactly the reason one can't divide by zero. Are you using some personal definitions of "off" "topic" and "here"?

It is quite pleasant being able to point out where scherzando is wrong without having the face the insults he throws at everyone who disagrees with him.

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15 minutes ago, studiot said:

...

He said that 0/0 is not a specific number.

...

Zero on the other hand is most decidedly a perfectly respectable number.

...

Zero is NOT a value. 10 is a value. Zero is a number without a value. This is what I mean and nothing more.

Infinity is NOT a value.

I have taken a great deal of math at college, years ago. I know how infinity is treated in mathematics.

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great deal

Is a great deal a value?

If so how much?

Are you going to answer my previous question?

4 minutes ago, studiot said:

Why couldn't you wait till I came back and finished my post as I promised?

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10 hours ago, studiot said:

Is a great deal a value?

If so how much?

Are you going to answer my previous question?

If you want an answer, then I will give it: 3 semesters Calculus, 1 Differential Equations, 2 Semesters Probability & Statistics, Numerical Analysis, 2 semester of Abstract Algebra (Group Theory). There are others, which I can't remember (early 80s), I should go find those, so I know for such questions. I entered the workforce as a computer programmer and did that for, total, 10 years.

My degree is a hybrid because my college did not--at that time--have a proper Computer Science major; mine is a B.A. is Computer Mathematics--but, as we all know, there is no software-dedicated mathematics.

I will go look for your "previous question."

Thanks.

10 hours ago, studiot said:

Why couldn't you wait till I came back and finished my post as I promised?

I don't understand this question. Oh I see, Are you aware that I have had multiple warnings for not replying under some undisclosed time-frame? Therefore, I don't give a bleep about waiting for you. I'm inches from being banned. You showed no sign of getting to what i posted.

Zero is NOT a value. 10 is a value. Zero is a number without a value.

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Quite simply: why should we care what is or isn't a "value"? We have a perfectly serviceable definition of "real number", or "integer number", or "whole number", or "natural number". And all of them include 0, and the corresponding definitions have a clear reason why division by 0 doesn't work.

The reason we can't divide by 0 is quite simple: multiplication by 0 isn't bijective. 0/0 doesn't make sense because 0 is the output of multiplication by 0 for multiple input values. 1/0 doesn't make sense because 1 is not the output of multiplication by 0 for any input value.

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10 hours ago, uncool said:

The reason we can't divide by 0 is quite simple: multiplication by 0 isn't bijective. 0/0 doesn't make sense because 0 is the output of multiplication by 0 for multiple input values. 1/0 doesn't make sense because 1 is not the output of multiplication by 0 for any input value.

Thanks uncool, +1

I was coming round to expressing exactly that in less formal language and with longer explanation when I was so rudely interrupted.

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11 hours ago, uncool said:

Quite simply: why should we care what is or isn't a "value"? We have a perfectly serviceable definition of "real number", or "integer number", or "whole number", or "natural number". And all of them include 0, and the corresponding definitions have a clear reason why division by 0 doesn't work.

The reason we can't divide by 0 is quite simple: multiplication by 0 isn't bijective. 0/0 doesn't make sense because 0 is the output of multiplication by 0 for multiple input values. 1/0 doesn't make sense because 1 is not the output of multiplication by 0 for any input value.

Not quite simply. Do you dispute my reason? You can't dispute my reason. You haven't disputed my reason. Your reason, I do not dispute. My reason gets to the exact heart of the matter. Your reason does not. Do you understand the several assertions I have made?

1 hour ago, studiot said:

Thanks uncool, +1

I was coming round to expressing exactly that in less formal language and with longer explanation when I was so rudely interrupted.

Please see the beginning of this post.

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