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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


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


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

Perfect measure


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