On Mon, Dec 5, 2011 at 4:33 PM, saurabh singh <saurab...@gmail.com> wrote:
> 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.* What about addition of real numbers then. Real numbers are uncountably infinite. > > > On Mon, Dec 5, 2011 at 4:26 PM, Aamir Khan <ak4u2...@gmail.com> wrote: > >> >> >> On Mon, Dec 5, 2011 at 3:31 PM, saurabh singh <saurab...@gmail.com>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 algogeeks@googlegroups.com. >>> To unsubscribe from this group, send email to >>> algogeeks+unsubscr...@googlegroups.com. >>> 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 algogeeks@googlegroups.com. >> To unsubscribe from this group, send email to >> algogeeks+unsubscr...@googlegroups.com. >> 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 algogeeks@googlegroups.com. > To unsubscribe from this group, send email to > algogeeks+unsubscr...@googlegroups.com. > 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 algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
