Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Two Different Reasons.

Both a/0 (where a does not = 0) and 0/0 are undefined, but for different reasons. Explain the different reasons in your own words.

Let me see.

I say a/0 is undefined because division by zero is not possible.

I say that 0/0 is undefined because 0/0 is indeterminate.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Two Different Reasons.

Yes but would you be satisfied if someone used your words to 'explain' these things to you?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Two Different Reasons.

Yes but would you be satisfied if someone used your words to 'explain' these things to you?

Bob

Let me say it this way. Explain the different reasons using mathematics.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 255

Re: Two Different Reasons.

And what about (a/0)/(b/0)? [∞/∞]?

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Two Different Reasons.

And what about (a/0)/(b/0)? [∞/∞]?

One question at a time.

Let a = any integer

Then 0/a = 0.

Let b = any integer

Then b/0 = undefined. Division by zero DNE

I think infinity/infinity = indeterminate.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Two Different Reasons.

The first depends on the context. Sometimes it could be a/b.

Later edit.  I think folk are missing the point of the original question.  Teachers use this sort of question to get the student to think carefully about their own understanding of the ideas.  What actually is it that makes these divisions
impossible to complete. It forces you to confront what we mean by division and that pushes us towards multiplication.

I would start with one we can do eg 6 x 8 = 48 implies that 48 divided by 6 = 8 so we could say "What do you have to multiply 6 by to get the answer 48?"

So what do you have to multiply 0 by to get the answer 6?

And the other one what do you have to multiply 0 by to get the answer 0?

As for (a/0)/(b/0) if this is the limit of (a/delta x)/(b/delta x) as delta x tends to 0, then a/b is  good answer.

And infinity/infinity ?  Where did that comes from? As infinity doesn't obey the rules of arithmetic it shouldn't be occurring in a division calculation. But if we're trying to sketch y = (x^2 +3)/(x-2) and want to know what happens as x tends to infinity then we can say this tends to x making the line y=x an asymptote.

Bob

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Keep_Relentless

Member

From: Queensland, Australia

Registered: 2024-05-05

Posts: 61

Re: Two Different Reasons.

I picked up somewhere that the result of a division represents how many times you need to subtract the divisor from the dividend to get zero. So 15/5 = 3 because 15-5-5-5 three times = 0.

This suggests a/0 is unanswerable because it's a meaningless question, because you'll never get a to 0 by subtracting 0 from it.

Similarly with 0/0, this time you'll get 0 for ANY number of subtractions, so again there's no meaningful answer.

Maybe there are other explanations and applications of assigning answers to them but that's how I wrap my head around it.

K_R

---

"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Two Different Reasons.

The first depends on the context. Sometimes it could be a/b.

B

If it's a/b, b cannot be zero. I understand that it's ok for a to be 0.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Two Different Reasons.

I picked up somewhere that the result of a division represents how many times you need to subtract the divisor from the dividend to get zero. So 15/5 = 3 because 15-5-5-5 three times = 0.

This suggests a/0 is unanswerable because it's a meaningless question, because you'll never get a to 0 by subtracting 0 from it.

Similarly with 0/0, this time you'll get 0 for ANY number of subtractions, so again there's no meaningful answer.

Maybe there are other explanations and applications of assigning answers to them but that's how I wrap my head around it.

K_R

A. 0/0 does not = 0. The answer is said to be indeterminate. Do you know why?

B. If a is any integer, then 0/a = 0.

C. If a/b is a rational number, then b cannot be 0 because division by 0 DNE.

D. Of course, if a represents any integer, then a/0 is undefined or DNE.

DNE = DOES NOT EXIST

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Two Different Reasons.

Please see my edited post 6.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Keep_Relentless

Member

From: Queensland, Australia

Registered: 2024-05-05

Posts: 61

Re: Two Different Reasons.

I would try to explain A. by saying it looks like on any standard view of division there is no basis for privileging any answer to 0/0 over any other answer. It's indeterminate because it could be anything.

I would be starting to get a bit out of my depth though.

K_R

---

"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

Keep_Relentless

Member

From: Queensland, Australia

Registered: 2024-05-05

Posts: 61

Re: Two Different Reasons.

Hey Bob,

Makes sense. I thought of a question. Is the only reason mathematicians do not say 0/0=17 is true and 0/0=-4.5 is true and 0/0=phi is true; is that reason because we could then derive 17=-4.5=phi from it?

So basically indeterminacy is jargon for it could be this or that but this and that aren't the same, therefore we're not going to assign a value to it. Except in the right context.

---

"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Two Different Reasons.

Please see my edited post 6.

Bob

Copy.