16 May '15 02:53>
Originally posted by FabianFnasPossibly we should talk about what these things are, rather than squabble over definitions. An interesting point about Turing machines is that the space of automorphisms of the natural numbers is uncountable, but there are only a countable number of programs. The space of automorphisms are functions of the form:
So if we use one definition instead of another - does this mean that those people who make a living out of it earn less cash? In short - does it matter much?
I say the definition is just an opinion. The writer of the article has one opinion, you have an another opinion. And you say it matter - how?
If you want ENIAC to be the first computer, then yo ...[text shortened]... rs. I stick with the opinion that it just doesn't matter. And see - the world didn't fall apart.
f: ℕ→ℕ
and it's fairly easy to see that this is uncountably infinite by considering the order of the permutation group. The number of possible programs, however, is just the number of numbers since any program is just a string of binary digits and therefore equivalent to a natural number. One of the consequences of this is that there are numbers which are not computable.