# Category:Mathematical Induction

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This category contains results about **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 $w_0$.

## Also see

## Subcategories

This category has the following 11 subcategories, out of 11 total.

### D

### F

- Forward-Backward Induction (2 P)

### P

- Proof by Superinduction (1 P)

### T

- Transfinite Induction (10 P)

### W

## Pages in category "Mathematical Induction"

The following 17 pages are in this category, out of 17 total.