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!

Induction Proof

  1. Jan 13, 2009 #1
    I'm just wondering if this is a legitimate proof by induction.

    Prove, for all natural numbers [tex]n[/tex], that [tex]2^n>n[/tex]

    Proof. For [tex]n=0[/tex], [tex]2^0=1>0[/tex] and for [tex]n=1[/tex], [tex]2^1=2>1[/tex]. Similarly, if [tex]n=2[/tex], then [tex]2^2=4>2[/tex]. Now assume [tex]n>2[/tex] and we have proven the result for [tex]n-1[/tex]. We must show it is true for [tex]n[/tex].

    We have:



    The last inequality follows from the fact that [tex]n>2[/tex].

    I'm worried about the fact that I have more than one base case. Is this still alright?
    Last edited: Jan 13, 2009
  2. jcsd
  3. Jan 13, 2009 #2
    Looks right. Doesn't matter how many base cases you have as long as you cover all natural numbers in the end.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Induction Proof
  1. Proof by induction (Replies: 2)

  2. Proof by induction (Replies: 9)

  3. Proof by induction (Replies: 32)

  4. Induction Proof (Replies: 14)

  5. Proof by Induction (Replies: 6)