Cookie: In Dutch it's called "inductie" (used Wikipedia to get it).
It's a special kind of math, so I suggest you don't start doubting
Example:
Show that 1+2+3+...+n = (n(n+1))/2 is true when n is a positive integer.
You would solve that this way:
1. n=1, both sides equal 1, so it's true.
2. Assume that it is true for n=k, so if it is true for k+1 we have prooven it's always true.
3. We prooved that 1+2+3+...+k is (k(k+1))/2 is the first step, so we can replace the set of numbers with that expression. We get
(k(k+1))/2 + (k+1) = ((k+1)(k+2))/2
Then you solve the right and left side separately, in this both are
(1/2)k^2 + (3/2)k + 1
We have now prooven it's true using induction
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