[Solved]: Can a computer count to infinity?

Problem Detail: 

So, could a computer count to infinity assuming it was a super computer and had near unlimited amounts of ram and hard drive/solid state drive storage? I am being serious when I ask this.
[This is what I am asking]: Wouldn't Infinity mean endless counting, and wouldn't that be infinity?

Asked By : mathworks

Answered By : Ran G.

It depends on what you mean by "count to infinity". Specifically, how does the computer give output?

consider the following quesitons:

• Can a computer show, on its screen, all the number from 1 till (infinity): increasing the number on screen by 1 every second?
• Can a computer send on the network line, a package that contains a number starting with 1, and increasing the number by 1 every second (splitting large numbers into multiple packages, assuming computation is very fast, and "every second" can be "every minute", etc, as necessary)

then, the answer for the above is YES.

However,

• can a computer hold (in his memory/RAM/HD/whatever finite storage unit it connects to) a number, so that it starts with 1 and increase this number every x seconds?

then the answer is NO. At some point, the computer will be out of storage. This is because the storage is finite, and "counting to infinite" requires an infinite amount of information.

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Question Source : http://cs.stackexchange.com/questions/43937