Identifying when we can use an inductive proof

Imagine a line of dominoes. If you knock over the first one, and each domino is close enough to knock over the next one, then all the dominoes will fall. Proof by induction works similarly. We want to prove something is true for all numbers (or all numbers greater than a certain value). To do this, we need two things:

The Base Case: We show the statement is true for the first number (like knocking over the first domino).
The Inductive Step: We show that if the statement is true for some number, then it must also be true for the next number (like showing that each domino will knock over the next).

If we can prove both of these, then the statement must be true for all the numbers we're considering. Sometimes it's easy to see how to set up our proof, and sometimes it takes a little more work. And sometimes, induction isn't the right tool at all.

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