# Perfect

Main forms: *perfect*, adjective.

Related forms: *perfectness* (extent to which something is perfect), *perfection* (being perfect)

Typical use:

- The best; something that cannot be improved further, something that fits the requirements exactly. Similar words: ideal, optimal
- Something pure, unsullied, without any tainting influences. Similar words: pure, ideal, isolated

## Contents

## Economics

In economics, *perfect* is typically used in the sense of *ideal*, or *as good as it can get*.

**Perfect information** (also called **complete information**): Perfect information refers to a situation in a game where, at any given time, every player has complete information about the game. Equivalently, there is no existing piece of information that can be given to a player to make that player play better. The term is used in economics to describe a situation where all people in an economic transaction or market, have complete information.

No related subject wiki entry.

Also located at: Wikipedia:Perfect information

**Perfect competition** (also called **pure competition**): A market form where no buyer or seller can perceptibly influence the price of the good. It usually occurs when there is a large pool of buyers, and a large number of competing sellers, for the same good.

Also located at: Wikipedia:Perfect competition, Britannica:Perfect competition

## Mathematics

### In group theory

**Perfect group**: A group that equals its own commutator subgroup (i.e. derived subgroup).

Main subject wiki entry: Groupprops:Perfect group

Also located at: Wikipedia:Perfect group, Mathworld:PerfectGroup, Planetmath:PerfectGroup

### In topology

**Perfect space**: A topological space where every point is closed, and is an intersection of countably many open subsets containing it.

Main subject wiki entry: Topospaces:Perfect space

**Perfectly normal space**: A normal space where every closed subset is an intersection of countably many open subsets containing it.

Primary subject wiki entry: Topospaces:Perfectly normal space

Perfect set: A set in a metric space that has no isolated points.

### In number theory

**Perfect power**: A natural number expressible as , where are natural numbers and

For , termed a **perfect square**. For , termed a **perfect cube**.

No relevant subject wiki entry.

Also located at: Wikipedia:Perfect power, Mathworld:PerfectPower

**Perfect number**: A natural number that equals the sum of all its proper (positive) divisors.

Primary subject wiki entry: Number:Perfect number

Also located at: Wikipedia:Perfect number, Mathworld:PerfectNumber, Planetmath:PerfectNumber

### In field theory

**Perfect field**: A field that either has characteristic zero, or has characteristic and for which the map is a surjective map. Equivalently, it is a field such that every algebraic extension field for it is separable.

Primary subject wiki entry: Galois:Perfect field

Also located at: Mathworld:PerfectField, Planetmath:PerfectField

### In graph theory

**Perfect graph**: A graph with the property that for every induced subgraph, the chromatic number equals the clique number.

**Term variations**: Strongly perfect graph

No relevant subject wiki entry.

Also located at: Wikipedia:Perfect graph, Mathworld:PerfectGraph

**Perfect matching**: A matching in a bipartite graph such that every element on one side gets matched to exactly one element on the other side.

No relevant subject wiki entry.

### In measure theory

## Physics

**Perfect conductor**: An electrical conductor with zero resistivity. Certain materials become perfect conductors below a certain temperature. A perfect conductor that also exhibits properties like the Meissner effect is called a superconductor. All known perfect conductors are superconductors.

No subject wiki entry.

Also located at: Wikipedia:Perfect conductor