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1. It depends on what you mean when you say 0.999999... (if you don't define what you mean, then there is nothing to debate really).

When people talk about "infinities", what they really mean is some kind of limit process, since the concept of "infinity" is very counter-intuitive and not mathematically rigorous. I interpret 0.999999... to mean the real number that is the limit of the geometric sum 0.9 + 0.09 + 0.009 + ... as you add more terms indefinitely -- which does equal 1 -- in the sense that given any arbitrarily small real neighborhood around 1 on the real number line, the sum will be confined to that neighborhood after a sufficient finite number of terms (which is easily calculated).

The real numbers are dense, so there is no such thing as "the biggest real number less than 1".

Now, if you don't interpret it that way, or if you don't believe in limits or that 0.999999... is a real number, then certainly you may get other results.

2. Originally Posted by smolloy

That proof is invalid (I think ). It only appears valid because people find it hard to imagine the endless number of 9's after the decimal point and so make computational errors when they try to think about it. This is a common problem that arises when trying to think about infinities. For example, infinity minus infinity is not zero -- mathematicians would call it "undefined". Similary with zero divided by zero.

0.999999...... is not 1. It's just as close as you can get without actually being 1.

I think.....
Indeed (you can only have an outcome from 10x if x is defined).
You can't use undefined numbers like that.
>so 0.999... x 10... is not 9.999... but ends at 0.999... x 10(your can't calculate it any further)

Originally Posted by spoon!
Now, if you don't interpret it that way
In maths, their's no room for interpretations.
It's either defined or not.

3. Originally Posted by jens
In maths, their's no room for interpretations.
It's either defined or not.
If you define one as first stop in infinity (addition, movement), than 1=1 (first) and not whatever was before or will be after.

4. \$spacer_open \$spacer_close
5. Originally Posted by pavlo_7
Originally Posted by jens
In maths, their's no room for interpretations.
It's either defined or not.
If you define one as first stop in infinity
You can't define that cause infinty itself is not defined.
This is also why people realy need to know the last number of Phi.

6. I will try to define infinity:

Infinity is time, and 1 is the first count of it

7. what the hell is the relevence of this?

8. I do not not know the answer myself.
I am just trying to have some fun (play a game) with this question about 1.
So here is what I came up with to continue my previous thought:

There is no need to define what causes time (infinity), because it would be a logical
error (there cannot be anything more than infinity, or less than infinity).
Infinity can also be viewed as something unlimited, or the complete opposite: o (zero)
1 is what breaks this pure infinity, therefore it must be defined in some way, and it must be exact, such as: 1=1 (no less and no more).
With introduction of 1, infinity does not exist anymore.
Zero in calculations only represents the infinity that existed before the introduction of 1.
The last number must be 1 added to the previous number, and that should be the limit of all calculations.
So, the limit would depend on how far you want to go adding 1 to the previous number.

jens: I hope you did not take it seriously

9. Originally Posted by pavlo_7
I do not not know the answer myself.
I am just trying to have some fun (play a game) with this question about 1.
So here is what I came up with to continue my previous thought:

There is no need to define what causes time (infinity), because it would be a logical
error (there cannot be anything more than infinity, or less than infinity).
Infinity can also be viewed as something unlimited, or the complete opposite: o (zero)
1 is what breaks this pure infinity, therefore it must be defined in some way, and it must be exact, such as: 1=1 (no less and no more).
With introduction of 1, infinity does not exist anymore.
Zero in calculations only represents the infinity that existed before the introduction of 1.
The last number must be 1 added to the previous number, and that should be the limit of all calculations.
So, the limit would depend on how far you want to go adding 1 to the previous number.
All very nice, but non of this counts in math. You obviously need a mathematical definition and not just a theory (It's really that easy).
One simply can't define infinity(think in numbers, not in words).

Originally Posted by pavlo_7
jens: I hope you did not take it seriously
I just wonder if the ones who made that did (I assume it's meant as a joke)

10. It all was a joke.
Edit: I actually agree with smolloy:
0.999999...... is not 1. It's just as close as you can get without actually being 1

11. Hmmm, I think everyone is missing the point here. It's not really important whether 0.999... == 1 or not, what is important is that you do the calculations on a open source platform, so that you can see whether the mathematics have been implemented correctly and with no security holes.

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