# Category:Definitions/Mathematical Induction

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This category contains definitions related to Mathematical Induction.

**Mathematical induction** is a proof technique which works in two steps as follows:

- $(1): \quad$ A statement $Q$ is established as being true for some distinguished element $w_0$ of a well-ordered set $W$.

- $(2): \quad$ A proof is generated demonstrating that if $Q$ is true for an arbitrary element $w_p$ of $W$, then it is also true for its immediate successor $w_{p^+}$.

The conclusion is drawn that $Q$ is true for all elements of $W$ which are successors of $w_0$.

## Pages in category "Definitions/Mathematical Induction"

The following 43 pages are in this category, out of 43 total.

### B

### I

### P

- Definition:Principle of Finite Induction/Also known as
- Definition:Principle of Finite Induction/Basis for the Induction
- Definition:Principle of Finite Induction/Induction Hypothesis
- Definition:Principle of Finite Induction/Induction Step
- Definition:Principle of Finite Induction/Terminology
- Definition:Principle of General Induction/Basis for the Induction
- Definition:Principle of General Induction/Induction Hypothesis
- Definition:Principle of General Induction/Induction Step
- Definition:Principle of General Induction/Minimally Closed Class/Basis for the Induction
- Definition:Principle of General Induction/Minimally Closed Class/Induction Hypothesis
- Definition:Principle of General Induction/Minimally Closed Class/Induction Step
- Definition:Principle of General Induction/Minimally Closed Class/Terminology
- Definition:Principle of General Induction/Terminology
- Definition:Principle of Mathematical Induction/Also known as
- Definition:Principle of Mathematical Induction/Basis for the Induction
- Definition:Principle of Mathematical Induction/Induction Hypothesis
- Definition:Principle of Mathematical Induction/Induction Step
- Definition:Principle of Mathematical Induction/Terminology
- Definition:Principle of Superinduction/Basis for the Induction
- Definition:Principle of Superinduction/Closure under Chain Unions
- Definition:Principle of Superinduction/Induction Hypothesis
- Definition:Principle of Superinduction/Induction Step
- Definition:Principle of Superinduction/Terminology

### S

- Definition:Second Principle of Finite Induction/Also known as
- Definition:Second Principle of Finite Induction/Basis for the Induction
- Definition:Second Principle of Finite Induction/Induction Hypothesis
- Definition:Second Principle of Finite Induction/Induction Step
- Definition:Second Principle of Finite Induction/Terminology
- Definition:Second Principle of Mathematical Induction/Also known as
- Definition:Second Principle of Mathematical Induction/Basis for the Induction
- Definition:Second Principle of Mathematical Induction/Induction Hypothesis
- Definition:Second Principle of Mathematical Induction/Induction Step
- Definition:Second Principle of Mathematical Induction/Terminology