History of Mathematics
Mathematical induction is a method of mathematical proof used to establish that a statement holds for all natural numbers. It involves two main steps: proving the base case, where the statement is verified for the initial value (often 1), and the inductive step, where one assumes the statement holds for an arbitrary natural number and then shows it must also hold for the next number. This technique is crucial in the development of algebraic notation and methods, as it helps formalize reasoning and demonstrates the validity of formulas across infinite sets.
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