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Mathematical Induction Help!

  1. May 7, 2012 #1
    I am currently exploring if whether or not a fourth dimension exists or can be drawn. According to my professor, I have to use mathematical induction.


    I know that 2^n is the equation and "n" equals the dimension. Therefore 2^1 is 2. The first dimension is a line with 2 terminal points and 2^2 =4 because the second dimension is four terminal points.

    For mathematical induction, I guess I'm trying to prove that 2^n is true and 2^n+1. The only way I can prove this is by drawing it. I can draw that 2^4 = 16 terminal points and 2^n+1, I can show that you can end up with 4 terminal points, 16 terminal points...However, I don't know what type of equation to use.
     
  2. jcsd
  3. May 7, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You need to use parentheses to make your expressions clear. For example, 2^4+1 = 16+1 = 17 when read using standard rules, but 2^(4+1) = 2^5 = 32. If you mean 2^(4+1), you need to write it like that, or else use the "superscript" button (on the pallette at the top of the input pane---it looks like X2); that would give you 24+1.

    RGV
     
  4. May 7, 2012 #3

    Mark44

    Staff: Mentor

    2n is not a statement, so it's meaningless to say that it is either true or false. Same with 2n+1.

    Examples of statements:
    x + 1 = 3
    y < 5
    The name of my dog is Dylan.

    Regarding the problem you posted, I don't believe that you have described it correctly. Induction proofs are not used to prove statements about specific value of n, such as n = 4. They are used to proved statements of a more general statement.

    What exactly are you trying to prove?
     
  5. May 7, 2012 #4
    Assume that the statement holds for n=1,.....n and show that it implies true for n+1
     
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