Re: Proof 0.999... is not equal to one.

chajadan@xxxxxxxx wrote:

What is the distance between 0.99999... and one?

Ciao

Karl

The distance is a non-real number I call a dubious number. It is of
indeterminate scale. It would take an infinity of them to equal one,
as mentioned at the end of my analysis. No real number increment would
be able to keep from surpassing one from zero in a finite number of
increments.

While the distance it not a real number, the system of real numbers
cannot allow 0.999... to be one as shown in my proof. In the Classic
Proof, 10x - x requires an element of subtraction that decimal cannot
hope to express in its own terms.

Bounds on the distance are not expressable in decimal notation.
Decimal notation, as described, is unable to express a large class of
real numbers. We know an infinity of numbers exist just after zero,
but decimal can only ever hope to express some reasonbly small
numbers. In between any smallest number decimal can express and zero
lie an infinity of inexpressable real numbers. These real numbers
would require only a finite mutliple to reach one.

Charlie,

I'm almost certain that you would be interested in "Is 0.999... = 1?",
Fred Richman, _Mathematics Magazine_ 72 (1999), 404-408. Based on what you
said above, I think that your ideas are quite similar to Richman's. His
article is also available on the web at

<http://www.math.fau.edu/Richman/HTML/999.htm>.

David
.

Relevant Pages

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