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Step 2 states that the statement is true for *n*=1.

Step 3 states that the only other thing needed is to prove that, whenever
the statement is true
for one number (say *n *= *k*),
it must also be true for the next number (that is, for *n *= *k*+1).

Steps 4 through 5 state that the only thing needed to accomplish this goal
is to
show that
everyone in an arbitrary group *G* of *k*+1 people has the same
age, under the assumption that, in every group of *k* people, everyone
has
the same age.

Step 13 states that this has been accomplished.

Therefore, from these steps, it follows that the statement is true for all
*n*.

Of course, we know it's not, so that means the fallacy must lie in one of the earlier steps.

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