Graduate Counting on a computing system

[thidmir]

TL;DR

I'm looking for any references on a device that is capable of counting over the set of natural numbers

It is plretty clear that a classical computer can't count over the set of natural numbers. If it is a digital device and you used an infinite loop you would eventually run out of memory space and have to reinterpret the meaning of the numbers (so it isn't really counting independently). An analog device can't either because even if you had an analog function like 1/n, you would need a sensitive enough detector to distinguish large enough values of n which goes against the Uncertainty principle. I've heard of some people trying to develop a machine that can count up to (though not including) infinity but does anyone know of any specific references?

 

[PeroK]

You cannot physically count all the natural numbers. You can only do it mathematically.

 

[jack action]

I've heard of some people trying to develop a machine that can count up to (though not including) infinity

It would count up to $\infty - 1$? How is that even possible? What is the value of $\infty - 1$?

A machine that would count to $\infty - 1$ would never stop until the end of time. And, at that time, couldn't we say that if it was built just 1 second earlier, or could have counted a little bit faster, that it could have counted at least one extra number?

 

[BvU]

I've heard of some people trying to develop a machine that can count up to (though not including) infinity

I have not, so I'd be grateful for any links ...

Your theme is quite interesting, though. But it makes me wonder: what exactly is counting? After a while just pronouncing the numbers would take endlessly long, so would it go towards an infinity squared business?
And how much is infinity minus half of that? So how long to count that?

$\$

 

[sysprog]

@thidmir, maybe it's time for you to check into Hilbert's Hotel for a fascinating visit.

 

[PeterDonis]

I've heard of some people trying to develop a machine that can count up to (though not including) infinity but does anyone know of any specific references?

If you've "heard of" it then you should be able to give at least one specific reference. If you can't, and apparently you can't, then we don't have a valid basis for discussion.

Thread closed.