An old topic revisited

[simonm]

Please don't everyone look away when they see this thread is about the old subject of whether 1 = 0.999... or not, I have a some more light to shed on the subject.

It relates to an argument that Guv posted in a previous discussion on this subject.
See thread here: http://www.vbforums.com/showthread.p...threadid=65922

Basically, Guv demonstrated a real number that was greater than 0.999... but less than 1 using hexidecimal notation. which basically evaulates to 0.FFF...

Most people were not conviced because they said that these two numbers both converged on the limit of 1 therefore they were the same.

But, if a similar argument is constructed using base20 notation (0 through J), it's self-evidency becomes clearer:

If I were to convert (base10)0.999... to base20, what would we have?

0.999...(Base10) = 

(Base10)     0.9      +     0.09   +   0.009         ....

=              18/20   +   18/200  +    18/2000  ....

(Base20)     0.i       +     0.0i     +  0.00i           ....

= 0.iii...(Base20)

But, since o.iii...(base20) must be less than o.jjj...(base20), we have therefore proved that there is a real number (that can't be represented in base10) that is greater than 0.999...(base10) but smaller than 1.

Is this valid?