sara242,
Restating what the paper purports to prove, and falsely claiming the paper proves it, does not make your argument valid.

Even if you use the non-standard term "non finite decimal" to mean an infinitely recurring representation of a rational number, IT IS STILL A FINITE NUMBER. Indeed even irrational numbers are finite despite the impossibility of representing their value with absolute precision. Only numbers with infinite value are not finite.

0.999... is the decimal representation of the fraction 9/9 (or 3/3 or 6/6 or 7/7 or 11/11 etc) and is equal to 1.
If you read http://en.wikipedia.org/wiki/Integer you'll see that they're defined by how they CAN BE written rather than how they ARE written. As 0.999... can be written as 1 it is an integer.

There is no contradiction and maths keeps going.

To Sara. The paper doesn't prove that different opinions and different logic are equal to eachother. But it does give a few different points to consider with math.

In math equal means that one side of the equal sign is equal invent and interchangeable with with the other side. For instance 5+7 equals and is interchangeable with 3+9. [5+7=3+9].

However not all forms of logic are interchangeable, nor all opinions interchangeable. They are not equal. Even within math there are different methods of logic that are not interchangeable. The example that 1+1=2 and 1+1=1 is a method of two different conclusions based on different logic applied. (One is an equasion with a vaule of adding two other numbers, the other is ignoring the numbers and saying that a number plus another number still equals only one number. The second reasoning is not accurately represented by 1+1=1 to show it's intent. The logic is not equally represented.

As for the 0.9999=1, that math logic is something that is above my knowledge. But if it is true, it is not applicable to other firms of logic. And perhaps even that math logic used two prove 10x=9x is only applicable in theory but not of value in practical use, thus not truly equal or interchangeable to the degree that it represents in the proof.

It was an intresting consideration, but it is not enough to say that all opinions are interchangeable.

Fact is
1 is a finite number it stops
A finite decimal is one that stops, like 0.157
A non-finite decimal like 0.999... does not stop
when a finite number 1 = a non-finite number 0.999.. then maths ends in contradiction

another way
1 is an integer a whole number
0.888... is a non-integer it is not a whole number
0.999... is a non-integer not a whole number
when a integer 1 =a non-integer 0.999... maths ends in contradiction

sara242,
Repeating your refuted claims doesn't make them true. They are not valid and never will be. I have already explained why what you label FACT is actually LIES.

I know you want maths to end in a contradiction. What I don't know is why. Is is just that you hate maths?

//Fact is
1 is a finite number it stops
A finite decimal is one that stops, like 0.157
A non-finite decimal like 0.999... does not stop
when a finite number 1 = a non-finite number 0.999.. then maths ends in contradiction

another way
1 is an integer a whole number
0.888... is a non-integer it is not a whole number
0.999... is a non-integer not a whole number
when a integer 1 =a non-integer 0.999... maths ends in contradiction//

Yeah... you've said already. Somebody reach over and give sara242 a thump, will ya? She seems to have got stuck.

Fact is the technology you keep repeating yourself relies on maths... and it works. Call off the alarms, folks, and dance a merry jig. For maths still works, oh frabjous day!

Dear Sara,

«1 is a finite number it stops»

1 is a finite number, but that has nothing to do with the fact that it stops.

«A finite decimal is one that stops, like 0.157»

All decimal numbers with a finite number of digits before the dot are finite, whether or not they stop.

«A non-finite decimal like 0.999... does not stop»

0.999... is finite: it is even less than 2.

«when a finite number 1 = a non-finite number 0.999.. then maths ends in contradiction»

Both are finite, so the above does not occur.

«1 is an integer a whole number»

Correct.

«0.888... is a non-integer it is not a whole number»

Correct.

«0.999... is a non-integer not a whole number»

Incorrect: 0.999... is an integer. This particular representation may not look like an integer, but it is.

«when a integer 1 =a non-integer 0.999... maths ends in contradiction»

However, "1" and "0.999..." are both integers, in fact they are two different representations of the same integer.