Mathematical proof of 0/0?

Question

can someone prove that 0/0=0
or 0/0=1 def of product or
0/0=undefine
anyone of these would be fine
thx in advance

Answer 1

ok.
PROOF

Let a and b NOT equal 0 and a does NOT equal b
then
a*0=0
b*0=0

Suppose 0/0 exists and is some value c,
then, if we divide both equations by 0 then
a = 0/0 and b=0/0
this would imply
a=c and b=c
BUT
we have defined a and b to NOT equal one another and not equal zero.
THUS
0/0 is undefined

END PROOF

this is "a proof by contradiction"
hope this helps!

Answer 2

First, let's clarify what all of the following are (which I've noticed some people have gotten horribly wrong):

0/1 = 0
1/0 = undefined
0/0 = indetermined

Zero divided by any non-zero number is zero. Remember that X divided by Y means "How many sets of Y can you make out of X objects?". For example, 24 divided by 8 is 3, because you can split up 24 objects into exactly 3 piles of eight objects each. So zero divided by some other number, say 5, means "How many sets of 5 objects can you make out of zero objects?" The answer is none, or zero.

Any non-zero number divided by zero is UNDEFINED. You can't divide by zero in math. If you could, then for example 5/0 would have some value. Call this x. But if 5/0 = x, then multiplying both sides by zero gives 5 = 0*x. But anything times zero is zero, so no value of x exists. So if we allowed division by zero, we'd get contradictions like this all over math. We can't have contradictions in math, so we rule out dividing by zero.

Or to put it another way, if you were trying to make "Groups of 0 out of 5 objects", you'd remove a pile of "zero" objects away and still be left with 5. You could repeat this forever, but never see your pile of 5 objects become any smaller. So once again, numbers like 1/0 are UNDEFINED.

The special case of 0/0 is called INDETERMINED, or in "indeterminate form" (but not "undetermined"). It is NOT the same thing as "undefined". This is because you can actually give 0/0 any value you want. For example, if 0/0 = x, then multiplying both sides by zero gives 0 = 0*x. So x can be anything, thus 0/0 can be anything. Again, the reason for the different name is because while 1/0 can't have ANY value, 0/0 can actually have EVERY value.

Another expression that is "indetermined" is 0^0. This is because you can rewrite it as 0^(n-n) = (0^n) / (0^n) for some positive integer n. But 0 raised to a positive integer power is just 0, so this becomes 0/0.

By the way, none of these values are "infinity" either, because infinity is just a concept and not an actual number.

Answer 3

Well, look at it this way:

Take the function f(x) = x / x. This function has the value 1 for all x not equal to zero. For x = 0 we don't know. However, we do know that, as x approaches 0, the limit of f(x) is 1.

Now consider the function f(x) = 0 / x. This function has the value 0 for all x not equal to zero. Again, for x = 0 we don't know. However, we do know that, as x approaches 0, the limit of f(x) is 0.

In summary, we have two functions approaching 0 / 0 as x approaches 0. In one, the limit is 1; in the other, the limit is zero. That's why 0 / 0 has to be considered undefined - the limit can be anything, as it all depends upon what function produces the 0 / 0.

Answer 4

nothing divided by nothing equals nothing....anything multiplied or divide by zero always equals zero or nothing...that is just the law of mathematics.

To simplify this would be take 4 X's 0= 0
Division are the same functions only in reverse of each other.

So 4/0 = 0

0x's0 =0
0/0=0
Nothing divided by nothing equals nothing
It's not undefined...it's nothing=zero

Answer 5

try to graph a divison of 0, it is infinite therefore undefined dog

Answer 6

if there's no candy shared by no ppl...so y will it equal to 1... but y not ZERO u say? cuz is it each people will get ZERO candy?...HELLOw! there's no ppl even....confusing? i noe...

here's a lame proof: try ZERO divided ZERO in the scientific calculater....mine says "MATH ERROR"... ;)

Answer 7

http://mathforum.org/dr.math/faq/faq.divideby0.html

It's undefined. See link for further details.

Answer 8

anything dividied by zero is zero, anything multiplied by zero is zero, anything plus zero is the same answer, anthing minus zero is the same answer! i hope this helps lolz?