# Is #1/oo = 0# ?

##### 4 Answers

#### Explanation:

Ex:

#1/10000000= 0.0000001

Now you can these number are not 1 and are not even relatively close to 0, but if you divide by a relatively huge number you will get a extremely small number which will nowhere be 0, but close to it.

As for anything times

See below.

#### Explanation:

As others have pointed out, it is an error to say that

If a fraction is formed by the ratio of

as the denominator increases without bound, the ratio approaches

Another way of saying this is:

If we divide

The precise mathematical definition takes a bit of work to understand:

we say that

For any positive number

for all

Notice that in the part after "if and only if" there is no mention made of infinity. We do not treat infinity as a number. (In spite of the phrase "as

We do use the notation

and read it "the limit as

The phrase "x approaches infinty" is easy to misunderstand and is best replaced by "x increases without bound".

I would like to use polar coordinates.

In polar form,

the direction making an angle

Upon this line

Let

Let us make

Now,

Cross multiply and take the limits.

Is it not understandable that, in either case, the indeterminate form

of (rf) is

covering both clockwise and anticlockwise rotations, for

Remember that the direction

#### Explanation:

There are only a few specialised contexts in which you can truly say

In calculus it is used as shorthand notation for limits.

In complex analysis and other interesting areas of mathematics it can have other meanings...

Consider a sphere with equation

This has centre

It "sits on" the XY plane at the origin, with the top point of the sphere being

Now consider lines passing through

Any such line will either intersect the plane at one point

Now suppose the XY plane represents the Complex numbers. Each

The unit circle corresponds to the equator of the sphere.

We now label the top of the sphere

This spherical representation of

We can define a few arithmetical operations involving

#z + oo = oo + z = oo# for any#z in CC#

#z * oo = oo * z = oo# for any#z in CC "\" { 0 }#

#oo * oo = oo#

#z/oo = 0# for any#z in CC#

#z/0 = oo# for any#z in CC "\" { 0 }#

The following are undefined:

#oo + oo#

#oo - oo#

#0 * oo#

#oo * 0#

With these restrictions

A MÃ¶bius transformation is a function of the form:

#f(z) = (az + b)/(cz + d)#

for some

Such a transform maps circles on