Definition:Principle of Mathematical Induction/Induction Hypothesis

Terminology of Principle of Mathematical Induction

Consider a Proof by Mathematical Induction.

The assumption made that $\map P k$ is true for some $k \in \Z$ is the induction hypothesis.

Also known as

The induction hypothesis can also be referred to as the inductive hypothesis.

Sources

• 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 0.1$. Arithmetic
• 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.3$ Inductive Proofs
• 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems ... (previous) ... (next): $\S 1.4.2$: Mathematical induction: Definition $1.29$
• 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.4$: Counting and mathematical induction: Definition $2.4.1$