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!

Proof rule

  1. Mar 9, 2013 #1
    Hello I'm learning about proofs and in my book there's a sect. On mathematical induction. And I'm trying understand why this makes it true for all values.
    Suppose that the formula is known to be true for n=1, and suppose that as a result of assuming that it is true for n=k, where k is an arbitrary positive integer, we can prove that it is also true for n=k+1.
    Then the formula is true for all k.

    Why does this addition of 1 make it true for all k?
  2. jcsd
  3. Mar 9, 2013 #2
    You know it's true for n=1 and you know that for every n where it's true, it's also true for n+1. Since you proved it for 1, this implies it's true for 1+1 = 2. Now, since you know it's true for 2, it must be true for 2+1 = 3. Now since you know it's true for 3, it's also true for 3+1 = 4. And so on, so it's true for every positive integer.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook