1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B Solve this math?

Tags:
  1. Nov 28, 2017 #1
    Let f(n) be of the form F(1) = 0.999999 F(2) = 0.9999999 F(3) = 0.99999999 Etc

    For arbitrary N >= 1

    Let g(n) = f(n)^2

    G(1) and g(2) end in 8

    By linear relation all g(n) end in 8

    Assume 0.999... = 1

    0.999... X 0.999... must end in 8 per (4)

    1 x 1 does not end in 8

    By (5),(6),(7), contradiction

    Therefore 0.999... = 1 is a contradiction
     
  2. jcsd
  3. Nov 28, 2017 #2

    Mark44

    Staff: Mentor

    No. How are you getting 8 as the final digit?
    Let's start in a more organized fashion.
    ##f_1 = 0.9##
    ##f_2 = 0.99##
    ##f_3 = 0.999##
    Then ##f_1^2 = 0.81##
    ##f_2^2 = 0.9801##
    ##f_3^2 = 0.99801##
    and so on. The sequence ##\{f_1, f_2, f_3, \dots \}## is approaching 1, which is easy to prove,
    and it can easily be shown that the sequence ##\{f_1^2, 4_2^2, f_3^3, \dots \}## also has 1 as its limit.
    No
    No.
    Thread closed.
     
    Last edited: Nov 28, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solve this math?
  1. Math problem. Solve it ! (Replies: 30)

  2. Solving math problems (Replies: 2)

Loading...