By A CooperHere's a nice fact about the natural numbers: Well-Ordering Principle. Every nonempty collection of natural numbers has a least element. Observe, before we prove this,... |induction

By A CooperInduction is like climbing a ladder. But there are other ways to climb besides ladders. Rock climbers don't just stand on one step. To get... |induction

By A CooperMany statements in mathematics are true {\em for any natural number}. For example. Fundamental Theorem of Arithmetic. Every natural number has a unique prime decomposition.... |induction

By A CooperMost informal definitions of the natural numbers call them the ``counting numbers". This is correct, but it's not a mathematical definition. To make a mathematical...