any number by itself is 1. then why is 0 by 0 = infinity ??

Answer 1

0/0 can have a meaning depending on how you got there. The key to solving the problem is limit values.
0/0 standing on is not useful, since you can't assign a value to it. But consider this: You have function f(x)=x/x Intuitively f(x) should equal 1 for any value of x. To prove this you use the limit value:
lim f(x) = 1
x->0
You would agree that 0.5/0.5=1, and that 0.001/0.001=1, and 0.00000001/0.00000001=1, all the way to almost 0/0.
The trick is to never let x be 0, but only let it get infinitely close.
You could also try the same for another function, g(x)=0/x, intuitively it should equal 0 for any x, and using the limit value, again let x come infinetely close to 0, but never let it be zero
lim g(x) = 0
x->0
So to wrap it up, 0/0 0/0 in itself never means anything, it can only mean something depending on the calculations you did to get there..

Answer 2

It isn't necessarily. It actually depends on how you approach this question.

For example:
If 0 * 0 = 0, then
0 = 0/0. Therefore some argue that 0/0 = 0.

On the other hand:
Let x = 0/0, then
x * 0 = 0. Therefore, some argue that since x=ANY VALUE makes this expression true, that the answer is "Undefined".

And yet others state:
0/0 = 1. Because any number divided by itself is 1. However, 0 is not truly a "number" - it is a null - a symbol we use to represent nothing (just like we use a side-ways 8 to represent infinity).

And finally:
Consider sin(x)/x^2, where x=0
The numerator and denominator "reach 0" at different rates, therefore the expression (with x=0), could be described as "infinity".

The problem is people are using "0" as a number, when it is really just a symbol to represent nothing -- just like the sideways 8 represents infinity. Applying operations and properties of normal real numbers to symbols will not yield predictable results.

Answer 3

Hi:

Okay the reason why any number divided by zero is infinity is to think about what division is :

Answer: it repeated subtraction or multiplication in reverse

lets look at it from the repeated subtraction view.

why is 10 divided by 5 equal 2 ?

10 -5 =5 (1), 5-5=0 (2) = so 5*2=10 or 5+5= 10. { ( ) kept track of of number of subtraction }

Now try it with 0 { in this case 10/0 }

10 - 0 = 10 (1) 10 - 0= 10 (2) , 10 - 0 = 10 (3)..... infinity

as you can see; it can never be subtracted down to zero by subtracting it by zero so the the number of subtraction is infinite

So that any thing divided by zero is infinite in the number of solutions

However is was once allow to say 0/0 = 1 due to the identity property of one in mathematics, they change that rule it seems at some time ago.

Answer 4

WRONG!
Division in the way you mean, is a function from two elements of a set of numbers (usually R), with the result an element from the same set of numbers.
Officially infinity is not a part of your set of numbers. It certainly is not part of R.
Apparently in the normal way we talk about division, the result of any number divided by zero is not possible. Officially said: If X is an element of R, then X divided by zero is not part of the set of divisions.

The reason why it is not possible to divide by zero (not even 0:0!) is because of the definition of the division function:
if A, B and C are elements from a set of numbers, then
A : B = C only if B * C = A
0 * infinity is not defined. You could of course define if as 0, but then you get a lot of troubles, because the multiplication function wouldn't be continuous anymore. A lot of calculations (integration, differentiation, etc) depend on the continuity of the set R. If you extend R such that multiplication is not a continuous function anymore, R would be a set without much use. Therefore it is common to let infinity not be an element of R

In physics and electronics it is quite often handy to extend R with the number infinity. A lot of phenomena can be described and explained easier by adding infinity. But remember: it's not official.

Answer 5

Using a non-zero number to divide by itself to get 1...
5/5=1

We can multiply both sides to get this equation...
5 = 1*5

In other words, 5/5 is 1 because 1 is what we'd multiply by 5 in order to get 5.

So, use the example with 0 instead of 5...

0/0=x
0 = x*0

The question is, what number can we substitute in for x to multiply by 0 in order to get 0? The answer is that ANY number will make this equation valid. In that sense, 0/0 can equal anything and so it's considered to be "indeterminate", and not really infinity.

Answer 6

Is there a typo in your question?

If you are saying any number (except zero) divided by itself is 1, then why is 0 divide by 0 = infinity?

First off, 0/0 is not equal to infinity.

Additionally, 0/0 is also not equal to 1.

In mathematics, 0/0 is undefined. You cannot put a meaningful value to it.

Answer 7

0 by 0 is undefined. the limit of 0 / x as x approaches 0 from the right is infinity. 0/0 is not infinity.

Answer 8

Maybe you are right. Then let us assume 0 / 0 = 1.

Now, lets see, 0 into any number is zero. [ You have to agree ]
So, 0 * x = 0 [ x is any number ]
Dividing by 0 on both sides,

x = 0 / 0
So, 0 / 0 can be equal to any possible number.
This contradicts our assumption, that 0 / 0 = 1

So our assumption [ i.e. your query ] is wrong and 0 / 0 is infinity.

Answer 9

0 is nothing. So nothing by nothing is infinity. 1 is a number. 1 by itself is 1.

Answer 10

HI seetharam!if u r serious vid ur Q i cn help u out!
0/0 is not infinity as u said ...look....!!
1. Any no. dividing 0 is 0 i.e. 0/4=0(wen 0 is in numerator)
2. bt any no divided by 0 is infinity i.e. 4/0=infinity(wen 0 is in denominator)
Therefore ,for 0/0 we have both the cases i.e.0 is in numerator as well as denominatr,hence it is neither 0 nor infinity bt cnsidered as indeterminant form,its in 12stndrd Maths!