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Mathematics

Proof by Induction: Building Infinite Chains of Reasoning

Quick fact

Induction is equivalent to the well-ordering principle: every non-empty set of natural numbers has a least element. This principle turns a leap of faith into a rigorous proof that a statement holds for all positive integers, forming a chain of reasoning that stretches to infinity.

Why this is interesting

Imagine you can prove something true for the number 1, and you can prove that if it's true for any number, it must be true for the next. Would you then know it's true for every single counting number, even though you've only done two steps?