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The principle of induction says that, if the following two things are true

*S*(1) is true, and- For all natural numbers
*k*: if*S*(*k*) is true, so is*S*(*k*+1),

This step in the proof is simply asserting that part 1 above
has already been proven (this follows from step 2), and that therefore
proving part 2 is enough to prove that *S*(*n*) is true for all *n*.

Why don't you go back to the list of steps in the proof and see if you can identify which one is wrong, now that you know it isn't this one?

This page last updated: May 26, 1998

Original Web Site Creator / Mathematical Content Developer: Philip Spencer

Current Network Coordinator and Contact Person: Joel Chan - mathnet@math.toronto.edu