not HW but a question: zero over zero

amnkb · 2024-02-29 09:51:57

This isn't hw but a question:
I know 0/0 is indeterminant officially
but I guess lots of computer people are saying that 0/0 should be 1
Does anyone know if anything is changing now?
Do you think 0/0 will eventually be defined (in math) as 1?

Phrzby Phil · 2024-02-29 13:05:34

I've got degrees in Mathematics and Computer Science, and I've never heard this.

Just curious - what's your source for: I guess lots of computer people are saying that 0/0 should be 1

I'm sure k/0 will always be undefined for any value of k, including zero.

KerimF · 2024-02-29 13:15:58

What I know is that 2a/a becomes 0/0 if a=0. In this case 0/0 = 2
In other words, to know the value of 0/0, its origin needs to be known first.
In practice, 0/0 (as ∞/∞) comes (be the result) from an algebraic expression under certain conditions, otherwise it is just three consecutive letters 0, / and 0
In general, to solve f(x)/g(x) when their ratio becomes 0/0 for x=a, we calculate f'(a)/g'(a). If f'(a)/g'(a) becomes 0/0 too, we calculate f''(x)/g''x)... and so on.

Bob · 2024-03-01 03:56:16

In number theory division is defined as the inverse operation to multiply. So if a times b = c then c/a = b
As 0 times n = 0 for all n, that suggests 0/0 = n.

Clearly that means 0/0 can be anything so mathematicians are never going to be able to accept a single value; too much mathematical theory falls apart if that is allowed.

The way the definitions get around the issue is to disallow division by zero entirely .

There are circumstances where a value can be assumed such as in differential calculus .

Bob

.

Phrzby Phil · 2024-03-02 07:49:26

KerimF wrote:

In general, to solve f(x)/g(x) when their ratio becomes 0/0 for x=a, we calculate f'(a)/g'(a).

The rule you mention here is L'Hopital's rule, which does NOT calculate "f(x)/g(x) when their ratio becomes 0/0 for x=a"
but rather calculates the LIMIT of f(x)/g(x) as x approaches a where f(a)/g(a) is indeterminate.

That limit may well exist, even if f(a)/g(a) is undefined.

E.g., The graph may be smooth but with a hole at f(a)/g(a).

The graph of (x^2 -3x + 2)/(x-2)
looks like the straight line y = x-1, but (e.g., in Desmos) hover over the line at x=2 and it will tell you (2,undefined).

This is an example of two functions equal at all but a finite number of points.

Last edited by Phrzby Phil (2024-03-02 08:01:44)

KerimF · 2024-03-03 03:12:07

Phrzby Phil wrote:

KerimF wrote:
In general, to solve f(x)/g(x) when their ratio becomes 0/0 for x=a, we calculate f'(a)/g'(a).
The rule you mention here is L'Hopital's rule, which does NOT calculate "f(x)/g(x) when their ratio becomes 0/0 for x=a"
but rather calculates the LIMIT of f(x)/g(x) as x approaches a where f(a)/g(a) is indeterminate.
That limit may well exist, even if f(a)/g(a) is undefined.
E.g., The graph may be smooth but with a hole at f(a)/g(a).
The graph of (x^2 -3x + 2)/(x-2)
looks like the straight line y = x-1, but (e.g., in Desmos) hover over the line at x=2 and it will tell you (2,undefined).
This is an example of two functions equal at all but a finite number of points.

You are right.

But, to me in the least (in practice), if I have f(x)= (x^2 - 3x + 2) / (x - 2) and x -> 2, f(x) -> 1. And the answer '1' is the required result.
For instance, my interest in math when I was at school (then universities) was to use it (after graduation) in designing real things; I ended up using it in electronics, hardware and software.
For example, math says that the voltage (as 5V) of a charged capacitor (C) while being discharged by a resistor (R) reaches 0V at infinity. In practice (not math), we can say that, in general, it could be seen as being 0V after 10*R*C sec only, instead of infinity.

But I also understand that, at school, students (including the one I was for about 20 years) have to follow the various definitions and rules that are approved by their teachers (who give them the grades).
My teachers now are those who buy my designed products

mathxyz · 2024-03-03 18:29:31

Bob wrote:

In number theory division is defined as the inverse operation to multiply. So if a times b = c then c/a = b
As 0 times n = 0 for all n, that suggests 0/0 = n.
Clearly that means 0/0 can be anything so mathematicians are never going to be able to accept a single value; too much mathematical theory falls apart if that is allowed.
The way the definitions get around the issue is to disallow division by zero entirely .
There are circumstances where a value can be assumed such as in differential calculus .
Bob
.

I thought 0/0 = indeterminate form. Yes?

Bob · 2024-03-03 21:07:37

Generally yes. But sometimes an actual value can be determined.
For example, it can be shown that sin(x)/x tends to 1 as x tends to zero provided x is measured in radians (rather than degrees).

The result makes it possible to differentiate sin(x) and from that all the other trig functions.

If x is in degrees the expression still tends to a number, just not 1.

Bob

KerimF · 2024-03-03 23:16:59

FelizNYC wrote:

Bob wrote:
In number theory division is defined as the inverse operation to multiply. So if a times b = c then c/a = b
As 0 times n = 0 for all n, that suggests 0/0 = n.
Clearly that means 0/0 can be anything so mathematicians are never going to be able to accept a single value; too much mathematical theory falls apart if that is allowed.
The way the definitions get around the issue is to disallow division by zero entirely .
There are circumstances where a value can be assumed such as in differential calculus .
Bob
.
I thought 0/0 = indeterminate form. Yes?

Yes, this is true in math only, not in real life.
In most 'real' cases, absolute 0 doesn't exist; like saying zero friction (in physics) or zero resistance (in electricity).
In other words, 0/0 is indeterminate when it has no physical/real history. Otherwise, it usually has a practical value. For example, 3*x/x = 3 when x = 0 (actually very close to 0, as in real life).
Therefore, in the integer domain (Z), 0/0 is indeterminate always.

mathxyz · 2024-03-04 01:38:31

KerimF wrote:

FelizNYC wrote:
Bob wrote:
In number theory division is defined as the inverse operation to multiply. So if a times b = c then c/a = b
As 0 times n = 0 for all n, that suggests 0/0 = n.
Clearly that means 0/0 can be anything so mathematicians are never going to be able to accept a single value; too much mathematical theory falls apart if that is allowed.
The way the definitions get around the issue is to disallow division by zero entirely .
There are circumstances where a value can be assumed such as in differential calculus .
Bob
.
I thought 0/0 = indeterminate form. Yes?
Yes, this is true in math only, not in real life.
In most 'real' cases, absolute 0 doesn't exist; like saying zero friction (in physics) or zero resistance (in electricity).
In other words, 0/0 is indeterminate when it has no physical/real history. Otherwise, it usually has a practical value. For example, 3*x/x = 3 when x = 0 (actually very close to 0, as in real life).
Therefore, in the integer domain (Z), 0/0 is indeterminate always.

I know the idea of 0/0 is important in calculus.
You said that 0/0 does not apply to real life events.
In elementary school, math teachers teach fifth graders that 0/0 = 1.
Back in the 1970s, this idea of 0/0 = 1 did not make sense.

Last edited by mathxyz (2024-03-04 22:09:48)

KerimF · 2024-03-04 03:30:13

FelizNYC wrote:

I elementary school, math teachers teach fifth graders that 0/0 = 1.
Back in the 1970s, this idea of 0/0 = 1 did not make sense.

You are right, saying 0/0 is equal 1 always doesn't make sense, in math also in applied math (in real applications).
But we like it or not, it is well known that 'the boss is always right' and the boss's student is his teacher.

This is why I never argued with any of my teachers about what he taught me, even if I was very sure he is wrong about something.
I simply let my teachers hear what they like to hear while I saved every idea that looked right to me in my set of knowledge and rejected whatever sounded wrong/illogical (to me). And the ideas which I wasn't sure about, I kept them pending for further studies.
After all, I am afraid that, in life, a truth (in math or else) may not please everyone.

mathxyz · 2024-03-04 22:34:28

KerimF wrote:

FelizNYC wrote:
I elementary school, math teachers teach fifth graders that 0/0 = 1.
Back in the 1970s, this idea of 0/0 = 1 did not make sense.
You are right, saying 0/0 is equal 1 always doesn't make sense, in math also in applied math (in real applications).
But we like it or not, it is well known that 'the boss is always right' and the boss's student is his teacher.
This is why I never argued with any of my teachers about what he taught me, even if I was very sure he is wrong about something.
I simply let my teachers hear what they like to hear while I saved every idea that looked right to me in my set of knowledge and rejected whatever sounded wrong/illogical (to me). And the ideas which I wasn't sure about, I kept them pending for further studies.
After all, I am afraid that, in life, a truth (in math or else) may not please everyone.

The truth hurts. Why do you think Jesus was hated so much back in His day? He spoke the truth because He is the truth. The same thing happens in today's society. I recently told one of my coworkers the truth about something she is doing in the building. What was that for? She hates me to the point of daily making false accusations hoping to get me fired or removed from the site. I cannot afford to let my guard down.
I spoke the truth and she cannot handle it.

KerimF · 2024-03-05 09:10:58

FelizNYC wrote:

KerimF wrote:
FelizNYC wrote:
I elementary school, math teachers teach fifth graders that 0/0 = 1.
Back in the 1970s, this idea of 0/0 = 1 did not make sense.
You are right, saying 0/0 is equal 1 always doesn't make sense, in math also in applied math (in real applications).
But we like it or not, it is well known that 'the boss is always right' and the boss's student is his teacher.
This is why I never argued with any of my teachers about what he taught me, even if I was very sure he is wrong about something.
I simply let my teachers hear what they like to hear while I saved every idea that looked right to me in my set of knowledge and rejected whatever sounded wrong/illogical (to me). And the ideas which I wasn't sure about, I kept them pending for further studies.
After all, I am afraid that, in life, a truth (in math or else) may not please everyone.
The truth hurts. Why do you think Jesus was hated so much back in His day? He spoke the truth because He is the truth. The same thing happens in today's society. I recently told one of my coworkers the truth about something she is doing in the building. What was that for? She hates me to the point of daily making false accusations hoping to get me fired or removed from the site. I cannot afford to let my guard down.
I spoke the truth and she cannot handle it.

A wise person doesn't blame her.

Those who are created to serve the world only, by building it or destroying it, are supposed to be guided by the preprogrammed instructions, embedded in their human living flesh, as it is the case of all other living things. These instructions are usually called instincts, as of survival, superiority, selfishness and applying a certain justice on others, to name a few. In other words, they cannot be free to oppose/defeat their natural robotic nature because they are created to be of the world and the world loves them.

Rare humans around the world who ended up being free to defeat, if they want to, their natural robotic nature, by loving even their enemies, by being humble towards everyone, by seeing other humans as an extension of their own existence and by not imposing any rules on them. Naturally, the world has no choice but to hate these free humans because they are no more of it.

After all, who hates or just blames a robot?

Kerim

Last edited by KerimF (2024-03-05 09:15:13)

amnkb · 2024-03-05 13:15:51

Phrzby Phil wrote:

Just curious - what's your source for: I guess lots of computer people are saying that 0/0 should be 1

I don't remember; its just something Ive seen from time to time

Bob wrote:

Clearly that means 0/0 can be anything so mathematicians are never going to be able to accept a single value; too much mathematical theory falls apart if that is allowed.

Yeh i've never heard math people say 0/0=1
More like computer ppl I think?

FelizNYC wrote:

In elementary school, math teachers teach fifth graders that 0/0 = 1.

wow
I never thot that anyone would say this to little kids!

FelizNYC wrote:

Back in the 1970s, this idea of 0/0 = 1 did not make sense.

I don't remember specifically where ive heard this but it was always a recent thing
I had no idea ppl were saying this so long ago
Thank youfor the info

mathxyz · 2024-03-05 18:30:13

amnkb wrote:

Phrzby Phil wrote:
Just curious - what's your source for: I guess lots of computer people are saying that 0/0 should be 1
I don't remember; its just something Ive seen from time to time
Bob wrote:
Clearly that means 0/0 can be anything so mathematicians are never going to be able to accept a single value; too much mathematical theory falls apart if that is allowed.
Yeh i've never heard math people say 0/0=1
More like computer ppl I think?
FelizNYC wrote:
In elementary school, math teachers teach fifth graders that 0/0 = 1.
wow
I never thot that anyone would say this to little kids!
FelizNYC wrote:
Back in the 1970s, this idea of 0/0 = 1 did not make sense.
I don't remember specifically where ive heard this but it was always a recent thing
I had no idea ppl were saying this so long ago
Thank youfor the info

Elementary school teachers have very little math training. In fact, indoctrination has totally ruined the public school system especially in large metropolitan cities overcrowded with minorities.

KerimF · 2024-03-05 21:05:33

FelizNYC wrote:

Elementary school teachers have very little math training. In fact, indoctrination has totally ruined the public school system especially in large metropolitan cities overcrowded with minorities.

It seems this is the case in almost all countries around the world.
I am afraid that a today's ordinary young person has to find ways to steal advanced scientific knowledge (unless his family is somehow rich), because, everywhere, ignorant people are easier to control than the well-educated ones.

So, during my school studies and high studies later, I wasn't looking for degrees but just good scientific knowledge, so that I could create my private business (which I did with an initial capital of what is equivalent to $100). So, after I passed well the MS eight courses (at the American University of Beirut, AUB) and my thesis was (still is) an innovative practical topology in communications (which I used in the 80's in my personal short-range RF links), I just returned home back to take care of my business (as a designer/producer in electronics).
But later I realized that I couldn't have the chance to do this if I was born in a mid-class family in what is known as the free world, because I would have no choice but to serve certain rich families (owning a certain big company related to electronics) by my knowledge.
For instance, at age 36, my father (who was brilliant in math) was hired to be the general manager of all branches in Middle East of a bank owned by certain French families. But about two years later, he was fired after he was a victim of a plot prepared by one of his older personnel to take his position. Unfortunately, his severe depression hit his two kidneys (in year 1959) and died soon after (I was 9). So, it became out of question for me to look for a job, for any position and any salary.

mathxyz · 2024-03-06 03:55:48

KerimF wrote:

FelizNYC wrote:
Elementary school teachers have very little math training. In fact, indoctrination has totally ruined the public school system especially in large metropolitan cities overcrowded with minorities.
It seems this is the case in almost all countries around the world.
I am afraid that a today's ordinary young person has to find ways to steal advanced scientific knowledge (unless his family is somehow rich), because, everywhere, ignorant people are easier to control than the well-educated ones.
So, during my school studies and high studies later, I wasn't looking for degrees but just good scientific knowledge, so that I could create my private business (which I did with an initial capital of what is equivalent to $100). So, after I passed well the MS eight courses (at the American University of Beirut, AUB) and my thesis was (still is) an innovative practical topology in communications (which I used in the 80's in my personal short-range RF links), I just returned home back to take care of my business (as a designer/producer in electronics).
But later I realized that I couldn't have the chance to do this if I was born in a mid-class family in what is known as the free world, because I would have no choice but to serve certain rich families (owning a certain big company related to electronics) by my knowledge.
For instance, at age 36, my father (who was brilliant in math) was hired to be the general manager of all branches in Middle East of a bank owned by certain French families. But about two years later, he was fired after he was a victim of a plot prepared by one of his older personI⁸nel to take his position. Unfortunately, his severe depression hit his two kidneys (in year 1959) and died soon after (I was 9). So, it became out of question for me to look for a job, for any position and any salary.

An interesting read. Thanks. Sorry about what happened to your dad. I too have been a victim of mean people who plotted against me to take my income and they did.

Math Is Fun Forum

#1 2024-02-29 09:51:57

not HW but a question: zero over zero

#2 2024-02-29 13:05:34

Re: not HW but a question: zero over zero

#3 2024-02-29 13:15:58

Re: not HW but a question: zero over zero

#4 2024-03-01 03:56:16

Re: not HW but a question: zero over zero

#5 2024-03-02 07:49:26

Re: not HW but a question: zero over zero

#6 2024-03-03 03:12:07

Re: not HW but a question: zero over zero

#7 2024-03-03 18:29:31

Re: not HW but a question: zero over zero

#8 2024-03-03 21:07:37

Re: not HW but a question: zero over zero

#9 2024-03-03 23:16:59

Re: not HW but a question: zero over zero

#10 2024-03-04 01:38:31

Re: not HW but a question: zero over zero

#11 2024-03-04 03:30:13

Re: not HW but a question: zero over zero

#12 2024-03-04 22:34:28

Re: not HW but a question: zero over zero

#13 2024-03-05 09:10:58

Re: not HW but a question: zero over zero

#14 2024-03-05 13:15:51

Re: not HW but a question: zero over zero

#15 2024-03-05 18:30:13

Re: not HW but a question: zero over zero

#16 2024-03-05 21:05:33

Re: not HW but a question: zero over zero

#17 2024-03-06 03:55:48

Re: not HW but a question: zero over zero

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