Working with the set of real numbers

Gregory Ewing greg.ewing at canterbury.ac.nz
Fri Feb 14 12:30:15 CET 2014


Devin Jeanpierre wrote:
> There is no way to iterate over all the reals one at a time, no matter
> how fast you execute instructions. If you could, it would be trivial
> to show that the reals have the same cardinality as the positive
> integers: correspond n with the whatever is returned by the nth call
> to it.next.

You're assuming that the calls to it.next are discrete
events separated by some nonzero time interval.

A decent transfinite processor would make a continuum
of calls, and execute uncountably many of them in any
finite period of time.

-- 
Greg



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