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Hi Folks

last weekend on another site i spent a fair bit of time trying to argue that 0/0=1 and getting nowhere

Does anyone here actually know what the answer is and if so can they provide the proof

the same thing applies for 0 to the power of 0 which should be 1 as all numbers rasied to the power of 0 are always 1

thanks for any help

0/0 is undefined because it has an infinite number of solutions. The idea that any number devided by iself is 1 is just a generalization, not a rule, and the same with anything to the 0th power.

gmiller wrote:0/0 is undefined because it has an infinite number of solutions. The idea that any number devided by iself is 1 is just a generalization, not a rule, and the same with anything to the 0th power.

I suppose new maths could be invented for it to be true

Can imaginary numbers be used here for the answer ie 0/0=1i

yes greg, what we we learned from grade school are;

* any anumber divide by itself =1
that is 3/3 = 1, 2/2 = 1, etc

* but any number divide by 0 = infinity
(try it in a calculator and it will give you a machine error)
that is 3/(1/100) = 300, 3/(1/10000) = 30000
meaning as the divisor get smaller the quotient gets bigger
and as the divisor approaches 0 the quotion approaches infinity.

What about the expression

x/x=1 though or is their a disclaimr along the lines of (x>0 x/x=undefined)?

The math symbol * 0 * is NOT a number but rather the absence of any
value and only acquires definition,or value,when used after an actual
number.
The principle that anything divided by itself equals one is not a generalization but a fact which simply has no application here because
*0* by itself is not anything,it is nothing.

x/y=z <=> z * 1/x = 1/y

make x and y equal but NOT 0, and you will notice that z = 1.

make x and y equal AND 0, and you will notice that z is undefined, because both 1/x and 1/y are 1/0, which IS undefined.

AND 0 is not a void, with the numbers 0, 0, 0, 0 (four zeros) you can create the value 24 using mathematical calculation. Just don't use division.
Should be prove enough.

How to create 24 out of 4 times nothing:

One of the first thing, is think a the big bang, how in a void there became 1 tiny dot which expanded and has actualy grown over our heads now.

Of coarse, we weren't there to LOG the event itself, but the result is showing that now existing one that we LOG started out as nothing.

Yes, Log (what_we_know) = 0 and repeated for all Noth's and added together all the "what_we_know" still adds to a very meager 4! to be factual.

To be precise, faculty or ! is the multiplying of every N number from 1 to n-th.

so 4! = 1 x 2 x 3 x 4 = 24.

Hmmm, big bang, yes

If I remember my calculus correctly, the mathematical proof involves the use of "limits". In essense, if you divide 1 (or any finite number) by successively decreasing divisors (e.g. 2, 1, 0.5, 0.0001, etc.), the results will be successively increasing numbers. Thus, as the divisor gets closer and closer to zero, the quotient (result) will also get bigger. Finally, as the divisor becomes zero, the result will be the biggest quantity, INFINITY.

It could just as easily be negative infinity, because if you come at it from the other direction -2, -1, -0.5..., your numbers are opposite from the other direction.

Division is not a "real" mathematical entity. It's the inverse function of multiplication. Since any number * 0 = 0, the equation 0*x=0 has an infinite number of solutions.

brn wrote:If I remember my calculus correctly, the mathematical proof involves the use of "limits". ...

using limits on 1/x with x approaching 0 from top or bottom is basic school-practice or learning.

Math dictates that any equation must be truly equal.
In speech you might say:
that part of a car is a wheel.

In math that would count as void because you can't state:
a wheel is part of that car

meaning:
0/0 = x ??? making x=1 seems intuitively correct, and checking back:
1 * 0 = 0; seems to proof it, but
x * 0 = 0; is correct for any x.
As is any other way you try to verify your calculation.

the same with:
x/0 = y ??? intuitively speaking y = 0 for any x.
mathematicaly speaking, x/0 does not contain any solution, because:
y * 0 /= x, unless it's the above case, with x=0.

simply said: x/0 IS undefined for any x.

Hi,

when reading this, I remember a nice math. equation (puzzle):

7=5+2
7 x (7-5) = (5+2) x (7-5)
49-35 = 35+14-25-10
49-35-14 = 35-25-10
7 x (7-5-2) = 5 x (7-5-2)
7=5


Where is the mistake

7-5-2=0 so you can't divide both sides by it.

There is simple answer to that question.

0/0 is *undefined*.

In standard arithmetic, 0/0 is *not defined* in the same way as 1/0 is *defined* as infinity, and in the same way that 2 is *defined* as symbol that represents result of addition 1 and 1 (i.e. 1+1 and 2 are the same thing written differently).

If, because of some reason, people decide that 0/0 is *defined* as 1, this may lead to some very strange results and perhaps we must start to learn whole (conventional) mathematics again. Similar will happen if we suddenly say that king in chess can move only on black fields; all chess opening theory will be invalidated.

On the other side, this can lead to some new exciting theories. Best sample is arithmetic of imaginary numbers that started with definition that square root of -1 is something called i; or non-euclid geometries (straight line is not straight anymore .

(I studied pure mathematic on the University).

shino wrote:There is simple answer to that question.

0/0 is *undefined*.

In standard arithmetic, 0/0 is *not defined* in the same way as 1/0 is *defined* as infinity

SNIP ...

(I studied pure mathematic on the University).

studied?
1/0 = infinity?
Your stretching some limits here now beyond their boundary.

tellymetwise wrote:

shino wrote:There is simple answer to that question.

0/0 is *undefined*.

In standard arithmetic, 0/0 is *not defined* in the same way as 1/0 is *defined* as infinity

SNIP ...

(I studied pure mathematic on the University).

studied?
1/0 = infinity?
Your stretching some limits here now beyond their boundary.

Ah, maybe I oversimplified things. Fortunately, you are here to put things on the right place.

shino wrote:

tellymetwise wrote:

shino wrote:There is simple answer to that question.

0/0 is *undefined*.

In standard arithmetic, 0/0 is *not defined* in the same way as 1/0 is *defined* as infinity

SNIP ...

(I studied pure mathematic on the University).

studied?
1/0 = infinity?
Your stretching some limits here now beyond their boundary.

Ah, maybe I oversimplified things. Fortunately, you are here to put things on the right place.

After jollyjumpers post you might say you oversimplified things quite a lot.
For a mathematician it would seem that you stated that the sun revolved around the earth at a distance of 150 million Km in 24 hours, because the equations of the solar system looks better that way.

Since you brought astronomy into this. 1/0=a black hole.

"...it's turtles all the way down."

tellymetwise wrote:

shino wrote:

tellymetwise wrote: studied?
1/0 = infinity?
Your stretching some limits here now beyond their boundary.

Ah, maybe I oversimplified things. Fortunately, you are here to put things on the right place.

After jollyjumpers post you might say you oversimplified things quite a lot.
For a mathematician it would seem that you stated that the sun revolved around the earth at a distance of 150 million Km in 24 hours, because the equations of the solar system looks better that way.

Please read, for instance

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

thanx.

I have 0 apples, and I need to divide it up equally amoung 0 people. How many apples does each person get? Since you don't have any apples, they get no apples.

On the other hand, there are nobody to give the apples to. Even if you had apples (which you don't), the process of giving apples to 0 people (nobody) would be impossible.

In conclusion, I don't have a conclusion. It doesn't seem right, though, that zero people and zero apples divide into 1. Infinity doesn't seem right, either, because you can't give an infinite amount of apples to the people (you don't have any apples!)

My head hurts now.



Ciao,
DragonPower aka Jonathan Pettit

gmiller wrote:Since you brought astronomy into this. 1/0=a black hole.

"...it's turtles all the way down."

Amazingly, a black hole has light in it, but an A-hole doesn't.

dragonpower wrote:I have 0 apples, and I need to divide it up equally amoung 0 people. How many apples does each person get? Since you don't have any apples, they get no apples.

**SNIP**

DragonPower aka Jonathan Pettit

Why work with apples. Borrow any standard currency coin, one should be enough. As the mathematician knows how to explain it. Divide it by nobody. ae 1/0 and money comes pouring out of gmillers blackhole.
Don't forget to give the coin back afterwards, and don't pick up any money either for that matter. Else you'll be changing the formula back to 1/1

Switching to the subject of Infinity and currency now

it is possible to pay into the bank one pound take out a million pounds and the bank loses nothing

there is even a way to take out an infintie number of punds and the bank still loses nothing