> "bassam king karzeddin" <bassam@ahu.edu.jo> wrote in > message > news:22019165.1180601903492.JavaMail.jakarta@nitrogen. > mathforum.org... > > Re: What is wrong between decimal and fraction? > > Posted: May 28, 2007 6:01 PM Plain Text > Reply > > > > > > Dear All > > > > Mr King. > > > [...] > > Any positive real number (except one) is a unique > production of prime > > numbers with each prime raised to a non-zero > integer and therefore of > > unique decimal representation > > > > Factorisation is good. > > > Hence, the irrational numbers are all those numbers > that have endless > > decimal digital expansion in any number system, > provided that their > > terminating digits are not all zero > > > > Why?
From the early definition of the rational numbers, we can simply extend their concept, but with infinite integers, so the real number definition becomes as a ratio of two finite or infinite coprime integers
And this definition doesn't count (zero, one, infinity) as real numbers except by CONVENTION
> > > From this you can see now why (0.999...) is an > irrational number even we > > don't know its prime factorization and therefor > can't be equal to one > > > > [...] > > > > I'm not sure what this is, but it's not a sound > nd proof.
In my opinion, the proof is straight foreword from the definition only > > -- > Glen > > Regards
