Why 1/0 is infinity ???????? Please prove?

Answer 1

Well, for starters, 1/0 is NOT infinity

In most simple arithmetics, division by zero is called "undefined" or meaningless.

It can be seen to be infinity if you follow the sequence of:
1/ 0.1 = 10
1/ 0.01 = 100
1/ 0.001 = 1000
etc
as the denominator approaches zero, the result is increasingly larger and hence one might think that if the denominator was zero, the result would be infinity.

The trouble is that if you define anything divided by zero as infinity, you start to run into some paradoxes.

1/0 = infinity
and 2/0 = infinity
therefore 1/0 = 2/0
and so 1 = 2

Answer 2

This is getting kinda dumb, honestly. At least this one, as opposed to 0 = 1, actually has a sort-of correct idea inside it. Since the function 1/x can be made arbitrarily large by making positive values of x sufficiently close to 0, then the function tends toward infinity from that side. But by the same reasoning, 1/x tends toward negative infinity approaching 0 from the negative side. Wukles, why bother using 1^infinity, esp. since 1^infinity = infinity is another false claim, one which there is no reason to make? You could just say 1/infinity = 0, so 1/0 = infinity. That's wrong, too, but it's a simpler wrong.

Answer 3

Brian L is right in saying it's undefined, and his reasoning is what I'd argue as well. If you want to take a visual look at the problem, think of the slope of an almost-vertical line.

Suppose a line goes through the origin and (0.001, 1). The slope is 1 / 0.001 = 1000. Suppose it turns very slightly counter-clockwise and goes through the origin and (0.000001, 1). The slope is now 1000000. It doesn't take a huge leap to guess 1 / 0 is going to approach positive infinity.

The trouble comes when you realize that there's no rule stating 0 can only be approached from the positive side. If a line goes through
(-0.001, 1) and the origin, the slope is -1000... and when you get closer and closer to vertical, the slope approaches 1 / 0, or negative infinity.

So, which is it? Positive infinity or negative infinity? Since you can't have two different answers to a division problem, we say division by zero is undefined.

Answer 4

A better way to state this is that the limit of f(x) = 1/x approaches infinity as x → 0 (from the positive side, anyway).

To prove this, pick any x > 0. Then f(x/2) produces a number larger than f(x). So there is no limit to how large f(x) can get as x → 0.

Answer 5

i think who proved that 1=2 are false
maybe any number /0 = infinity
because X/0=X* 1/0=x*infinity
if x=0 then 0/0= 0*infinity =0
so :
1/0 = infinity
and 2/0 = infinity
therefore 1/0 = 2/0
0/0*1=0/0*2
so 0*1=0*2=0

Answer 6

It isn't infinity. It's indeterminate. You cannot divide by zero.

Here's why:
You have:
1/0 = ∞ Where ∞ is non-deterministic. i.e. ∞ doesn't have any finite value. Or we can say that its non deterministic. This is exactly why we say that dividing by zero is not- defined (as ∞ is a symbol for not defined) or infinite.

Is ∞ really not defined ? Well by definition ∞ is the largest value in number system. So if you try puting it any value say a very large one 1 billion raised to power 1 billion raised to power 1billion .... however large it may be I can say ∞+1 is > ∞ thus this value of ∞ is not the larget value as reqd by definition. thus ∞ is mathematically not defined (and hence no algebra rules on this value works).

so 1/0 = ∞ = not defined = infinity ( all different ways to say the same thing)

Answer 7

As Louise explained very well, 1/0 is undefined. Take for example 1/x.

Right hand limit i.e. as x tends to 0 from right side i. x is near to zero but however small it's more than zero.
Lim (1/x) = + infinity
x->0+

Left hand limit i.e. as x tends to 0 from left side i. x is near to zero but however small it's less than zero.
and
Lim (1/x) = - infinity
x->0-

So in theory Left hand limit should be equal to Right hand limit. But it's not the case here, therefore it's undefined.

Another example is 1/x^2 and x tending to zero. In this case it's infinity. So 1/(0*0) will be infinity because LHL and RHL both are +infinity.

And for other people who are saying
if 1/x = y then 1 = xy. It's true only when x is not equal to zero. In this case we have x = 0 therefore 1 can't be equal to xy.

Read more about inequalities athttp://www.purplemath.com/modules/ineqsolv.htm .

Answer 8

How many zero's can go into 1?
That is essentially what is meant by division.
For example 10/2. How many two's go into ten. (5)
So how many zero's go into 1.
some say infinity because you could say infinite zero would be the closest to equalling one but a more correct answer would be impossible because no number times zero equals infinity. Impossible undefined whatever

Answer 9

1/0 is 1 divided by 0 which is *not* infinity. it is Undefined as 0 does not go into any number

Answer 10

It isn't infinity. It's impossible. You cannot divide by zero.

Here's why:

A/B = X, right? That means that X*B = A (do the algebra)

So you want to have 1/0 = ∞

That would have to mean that ∞*0 = 1

Which is impossible. There is no number of times that you could multiply ∞, or any other number, by zero to get 1 as your result.

So, we say that dividing by zero is undefined.