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Blast into Math! ets of nummers: mathematical plaagrounds
3. The third step is the hardest: we must get the escalator to start moving! To do this, we prove
that the statement is true for n +1. This is like jumping up high and landing with a thump
on the escalator, and BOOM! The escalator starts moving. The mathematical magic, or
mathemagic is that the escalator never stops. This is because once we have completed these
three steps, induction means that the statement is true for all integers greater than or equal
to the base case. The three steps of induction prove that:
• the statement is true for n =1 (the statement is true for the base case)
• once the statement is true for some n ≥ 1, it is also true for n +1,
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