On Thursday, 20 February 2014 21:18:32 UTC+1, Zeit Geist wrote: > On Thursday, February 20, 2014 12:09:31 PM UTC-7, muec...@rz.fh-augsburg.de wrote: > > > > > Cantor's diagonal argument works exclusively in the domain of terminating sequences which he himself as proven to be countable. Therefore the notion of uncountability, as far as it is based on this argument (the others can be disproven too), is far from being successful (although he has dazzled many mathematicians) but is simply self-contradictory. > > > > > > > But, if you have an Infinite List of Terminating Decimals, then Anti-Diagonal will be an Infinite (Non-Terminating) Decimal, which is Not on the List, because Everything on the List is Finite.
Do you know an n such that b_n is infinite? Certainly not. If you have a list of finite entries like 1 11 111 ... then the diagonal cannot be longer than all entries because each of its digits is restricted to a finite index.
This is the point where potential infinity is proven (the list is potentially in finite) and actual infinity is claimed (a diagonal that is longer than every entry). Fraud.
Infinite diagonals can only result from finite definitions. Alas, there are only countably many.