Math Is Fun Forum

To Ricky!

But how can any Number become! or is an Integer Number if it starts as . < 1

To luca-deltodesco!

The problem is it's impossible to know how many 9's there are in total!! because it's an Infinite Number! ie No End!.............................................................................................................

LET,S MAKE THIS AS SIMPLE AS POSSIBLE!
CAN ANYONE SHOW HOW! USING MATH IT IS POSSIBLE TO MAKE A NUMBER THAT IS SMALLER THAN ANOTHER NUMBER BIGGER! WITHOUT USING ADDITION!
AS IN THE PROBLEM BELOW!

Infinite 0.9 (stage one) ( some how we have to make this part larger! ) = 1

Ricky!

The problem is! you have not answered the question below,using only the numbers I have put forward! its that simple!

Infinite 0.9 ( Bridge this Gap with Math Please! )1

lets see your Math to show how 0.9 (Jumps) to become 1 ? and please dont say it already is! because as we all know Infinite 0.9 (stage one) starts its life smaller than 1 why should! or how is it possible to change its value,when it's an Infinite Number!

A.R.B
SO LETS TRY AGAIN!!.........................................

Here is the Challenge!

Can anyone prove Infinite 0.9 = 1

The proof someone puts forward must be shown as a Mathematical Proof.
I can Prove Infinite 0.9 (Stage one) Starts with 0.9 which is less than 1 to Start with.
So for me to be proved wrong someone has to show the Mathematics on how to Bridge the Gap from 0.9 to 1.
This is all someone has to do?

Infinite 0.9 ( Bridge this Gap with Math Please! )1

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Ricky (the Moderator) has put forward

Let a = 0.999... throughout.
a is in A_0 = [0.9, 1]
a is in A_1 = [0.99, 1]
a is in A_2 = [0.999, 1]
a is in A_n = [0.999...n...9, 1]
Note that because of the infinite number of 9's, this statement will be true for any number of A_n.
But, A_0 is a subset of A_1 is a subset of A_2 is a subset of ... A_n is a subset of A_n+1 ...
Also, note that with any finite amount of 0.999..., we may get arbitrarily close to 1. Thus, for any e (epsilon) greater than 0, we may find a finite amount of 9's such that 1 - e < 0.999...
This means that any real number less than 1 is not in one of the A_n sets listed above. Also, any real number greater than 1 is obviously not.
However, by the nested interval property, and infinite series of intersections of closed intervals is non-empty. That is:
A_0 intersected with A_1 intersected with A_2 ....
Is not empty. But it contains no numbers less than 1 or greater than 1. Thus, it contains 1 and only 1. But remember that a is in every set A_0, ..., A_n, ... and thus, a = 1.
A.R.B
The problem with the above Proof?
Is that it does not show clearly! How to show...............

Infinite 0.9 ( Bridge this Gap with Math Please! )1

using the numbers above as a Math Equation etc.............
The only answer would be! What I have put forward below.

Infinite 0.9 ( Bridge this Gap with Math Please! )1
Infinite 0.9 (            + 0.1                  )= 1

The only problem with the answer above is that,it changes the Definition of an Infinite Number! ie having no end!
But its the only way to reach the Conclusion that Infinite 0.9 = 1 ?

So without using the above Answer?,can anyone show in a simple clear way!

Infinite 0.9 ( Bridge this Gap with Math Please! )1

So here is the Challenge!

Can anyone prove Infinite 0.9 = 1

The proof someone puts forward must be shown as a Mathematical Proof.
I can Prove Infinite 0.9 (Stage one) Starts with 0.9 which is less than 1 to Start with.
So for me to be proved wrong someone has to show the Mathematics on how to Bridge the Gap from 0.9 to 1.

This is all someone has to do?   Infinite 0.9 ( Bridge this Gap with Math Please! )  1

A.R.B

In the Real World I have tried to find the end of the Universe! but its just not there!
As a human I will not accept  there is an End! when I see the so called end of an Infinite Number,by the Magic of Infinite 0.999999999999......becoming 1?
I will know behind this there will always be more .999999999999999999's for Ever!

Its impossible for Infinite 0.9 to ever = 1

Beacause there will always be a difference of Infinite 0.1

A.R.B