Definition:Principle of Mathematical Induction/Induction Step

Terminology of Principle of Mathematical Induction

Consider a Proof by Mathematical Induction.

The step which shows that $\map P k \implies \map P {k + 1}$ is called the induction step.

Also presented as

Some sources present the induction step in the form:

$\map P {k - 1} \implies \map P k$

Also known as

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

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 $1.29$