Hmm that too be should be impossible but the problem is how will you give the input of real numbers on tape? Notice however that we can always make a restricted machine that works on a subset of real numbers.....(For example integers)
On Mon, Dec 5, 2011 at 4:37 PM, Aamir Khan <ak4u2...@gmail.com> wrote: > > > 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. > -- 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.
