I said *uncountably infinite.* *Integers are countably infinite.* *A countably infinite set will require finite number of states as we can arrange them in order.*
On Mon, Dec 5, 2011 at 4:26 PM, Aamir Khan <[email protected]> wrote: > > > On Mon, Dec 5, 2011 at 3:31 PM, saurabh singh <[email protected]> wrote: > >> I was wondering can we design a machine(Even hypothetical) that can find >> a *perfect square root *of any integer thats given to it. >> My logic why we can't is since there are uncountably infinite real >> numbers, there will be uncountably infinite numbers requiring infinite >> states on a turing machine.But since there are only finite number of >> states,we cant make such a machine.And since we cant make a turing machine >> for calculating the square root we cant make any computing machine for the >> same. >> I am not sure about my logic though.Thats why i have this doubt. >> >> Just a thought, If you are saying that there are infinite real numbers > then it will require infinite number of states on turing machine. So, the > same explanation holds for every arithmetic operation. If you talk about > addition then also there are infinite number of numbers so there must be > infinite number of states and so not possible to have such a machine > according to your argument but we do have such machines. > > My point is that you are wrong somewhere that since there are infinite > real numbers so we must have infinite number of states in turing machine. > > -- >> Saurabh Singh >> B.Tech (Computer Science) >> MNNIT ALLAHABAD >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Algorithm Geeks" group. >> To post to this group, send email to [email protected]. >> To unsubscribe from this group, send email to >> [email protected]. >> For more options, visit this group at >> http://groups.google.com/group/algogeeks?hl=en. >> > > > > -- > Aamir Khan | 3rd Year | Computer Science & Engineering | IIT Roorkee > > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > -- Saurabh Singh B.Tech (Computer Science) MNNIT ALLAHABAD -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
