Announcement

Collapse
No announcement yet.

does .9 repeating equal one?

Collapse
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

  • #31
    Originally posted by Frogger


    Man, the number 1 is the most interesting number out there.
    I know 1 is the lonliest number. Does that count?
    Life is not measured by the number of breaths you take, but by the moments that take your breath away.
    "Hating America is something best left to Mobius. He is an expert Yank hater.
    He also hates Texans and Australians, he does diversify." ~ Braindead

    Comment


    • #32
      Not necessarily. One could easily define a map between two sets as he wants to. I am not obliged to send 0.9999... to 1. In terms of cardinality, both sets have the same cardinal. There is a bijection between these sets (which does not send 0.999... and 1 to 1 because that would not be inyective)


      You've now said the same thing 4 times. I agree that the sets are bijective, butread what I wrote: I said that the standard map is not a bijection.
      12-17-10 Mohamed Bouazizi NEVER FORGET
      Stadtluft Macht Frei
      Killing it is the new killing it
      Ultima Ratio Regum

      Comment


      • #33
        Well, in metrics spaces "closed" is weaker than "complete" (i.e., a space which is complete is closed), but you are right: both sets are closed (in fact, they are complete)


        Under the standard metric for real numbers, all closed sets are complete (can't remember what this property is called).
        12-17-10 Mohamed Bouazizi NEVER FORGET
        Stadtluft Macht Frei
        Killing it is the new killing it
        Ultima Ratio Regum

        Comment


        • #34
          Quoted from Frogger:
          "You've now said the same thing 4 times. I agree that the sets are bijective, butread what I wrote: I said that the standard map is not a bijection."

          I have to said this 4 times because you told me that I was "absolutely and fundamentally wrong here".
          I thought that you were implying that the first thing was wrong, my excuses because of the misunderstanding.

          Comment


          • #35
            I think you guys have just discouraged me from ever taking a course in number theory...
            "Beauty is not in the face...Beauty is a light in the heart." - Kahlil Gibran
            "The greatest happiness of life is the conviction that we are loved; loved for ourselves, or rather, loved in spite of ourselves" - Victor Hugo
            "It is noble to be good; it is still nobler to teach others to be good -- and less trouble." - Mark Twain

            Comment


            • #36
              I responded too quickly. I scanned what you read, but the part about showing injection and surjection seemed badly written...and I assumed you were trying to prove that the standard map was bijection (especially since just in my last post I'd clarified what I was discussing)...

              Let's please stop now...

              Unless you can tell me what it's called to have the property that all closed subspaces are complete (like Rn is...)
              12-17-10 Mohamed Bouazizi NEVER FORGET
              Stadtluft Macht Frei
              Killing it is the new killing it
              Ultima Ratio Regum

              Comment


              • #37
                Number theory is different. This is Real Analysis (which number theory is based on, partly...)
                12-17-10 Mohamed Bouazizi NEVER FORGET
                Stadtluft Macht Frei
                Killing it is the new killing it
                Ultima Ratio Regum

                Comment


                • #38
                  Quoted from Frogger:
                  "Under the standard metric for real numbers, all closed sets are complete (can't remember what this property is called)."

                  That is because the real number system is complete and each closed set of a complete set is in itself complete.
                  But what about it?

                  Comment


                  • #39
                    Are you a math grad student or something, alofatti?
                    "The issue is there are still many people out there that use religion as a crutch for bigotry and hate. Like Ben."
                    Ben Kenobi: "That means I'm doing something right. "

                    Comment


                    • #40
                      Is that case? I'm not sure (been 3 years since I did Analysis III...)

                      Let me think.
                      12-17-10 Mohamed Bouazizi NEVER FORGET
                      Stadtluft Macht Frei
                      Killing it is the new killing it
                      Ultima Ratio Regum

                      Comment


                      • #41
                        "Are you a math grad student or something, alofatti?"

                        No, I am not. I study Computer Science.

                        Comment


                        • #42
                          Which branch? Theory, software engineering, etc?
                          "The issue is there are still many people out there that use religion as a crutch for bigotry and hate. Like Ben."
                          Ben Kenobi: "That means I'm doing something right. "

                          Comment


                          • #43
                            I like the way Squid put it, but it all seems like some sort of logical lapse.

                            I recognize Frogger's expertise, but I don't understand what he's saying. As I understand it 0.99... < 1, and if x<>y then x!=y.

                            Bear in mind I'm a history major, and make no claim that I'm correct in this. It just seems to make sense.
                            John Brown did nothing wrong.

                            Comment


                            • #44
                              Felch: I'm the same way, I'm looking at it more from a strictly logical point of view instead of mathematical.

                              The best way I've had it explained is 1/3 is 0.3 repeating.
                              1/3 + 1/3 + 1/3 = 1, but if 1/3 is 0.3 repeating only, then 1/3 + 1/3 + 1/3 = 0.9 repeating. But it's not, it's 1.
                              "The issue is there are still many people out there that use religion as a crutch for bigotry and hate. Like Ben."
                              Ben Kenobi: "That means I'm doing something right. "

                              Comment


                              • #45
                                That is a somewhat difficult question to answer since there are not branches of study over here.
                                We study general concepts from computer organization + theory + software engineering (aghh!!) and then we choose some some optative courses. That would, perhaps, qualify as specializations.
                                To be honest with you, I am not perfectly sure about what would be my specialization, I have taken extra courses in some logic themes, game theory and (very little) of computer graphics.

                                Comment

                                Working...
                                X