What is "parity"

Parity \Par"i*ty\, n. [L. paritas, fr. par, paris, equal: cf. F. parit['e]. See Pair, Peer an equal.]

1. The quality or condition of being equal or equivalent; a like state or degree; equality; equivalence; close correspondence; analogy; as, parity of reasoning. ``No parity of principle.''
   --De Quincey.

   Equality of length and parity of numeration.
   --Sir T. Browne.

2. Specifically: (Finance) Equivalence in value to the currency of another country.

3. (Physics) A property assigned to elementary particles, conceptualized as a form of symmetry, representing the fact that no fundamental distinctions can be observed between right-handed and left-handed systems of particles in their interactions, and supported by the typical observation that the total parity of a system is unchanged as particles are created or annihilated; however, certain interactions involving the weak force have been shown to violate the principle of conservation of parity.

4. (Physics) A property of the wave function of a system, which takes the value of +1 or -1, indicating whether the value of the wave function changes sign if each of the variables of the system is replaced by its negative.

5. (Med.) The condition of having borne a child or children, alive or dead.

6. (Math.) The property of being even or odd; as, 3 has odd parity, but 6 has even parity.

7. Hence: (Computers) The property of having an even or odd number of bits set to the value of 1 (as opposed to 0); -- applied to bytes or larger groups of bits in a data structure. It is used mostly in the process of parity checking. The parity of a data structure can be changed by changing the value of the parity bit.

1570s, "equality of rank or status," from Middle French parité (14c.) or directly from Late Latin paritas "equality," from Latin adjective par (genitive paris) "equal" (see pair (n.)). Meaning "condition in which adversaries have equal resources" is from 1955, originally in reference to the U.S.A. and the U.S.S.R.

Etymology 1 n. (context uncountable English) equality; comparability of strength or intensity. Etymology 2

n. 1 (context medicine countable English) The number of times a woman has given birth. 2 (context agriculture countable English) The number of times a sow has farrowed.

1. n. (obstetrics) the number of live-born children a woman has delivered; "the parity of the mother must be considered"; "a bipara is a woman who has given birth to two children" [syn: para]

2. (mathematics) a relation between a pair of integers: if both integers are odd or both are even they have the same parity; if one is odd and the other is even they have different parity

3. (computer science) abit that is used in an error detection procedure in which a 0 or 1 is added to each group of bits so that it will have either an odd number of 1's or an even number of 1's; e.g., if the parity is odd then any group of bits that arrives with an even number of 1's must contain an error [syn: parity bit, check bit]

4. (physics) parity is conserved in a universe in which the laws of physics are the same in a right-handed system of coordinates as in a left-handed system [syn: conservation of parity, space-reflection symmetry, mirror symmetry]

5. functional equality

Parity is a United Kingdom-based men's rights organisation, which describes itself as campaigning to promote and protect the equality of men and women under the law. Its main focus has been in the area of state pensions and associated benefits, and most of its notable successes have occurred in this field. The organisation was previously called Campaign for Equal State Pension Ages.

Principle of parity is a legal concept used in codecision procedure disabling one European institution from making decision without obtaining assent of the other institution engaged in the procedure.

Parity may refer to:

• Parity (physics), a symmetry property of physical quantities or processes under spatial inversion
• Parity (mathematics), indicates whether a number is even or odd
  • Parity of a permutation, indicates whether a permutation has an even or odd number of inversions
  • Parity function, a Boolean function whose value is 1 if the input vector has an odd number of ones
  • Parity flag in computing, indicates if the number of set bits is odd or even in the binary representation of the result of the last operation
  • Parity of even and odd functions
  • Parity bit in computing, sets the parity of transmitted data for the purpose of error detection
  • Parity file in data processing, created in conjunction with data files and used to check data integrity and assist in data recovery
• Parity (biology), the number of times a female has given birth
• Parity (charity), UK equal rights organisation
• Parity (law), legal principle
• Mental Health Parity Act, also applies to substance use disorder
• Purchasing power parity, in economics, the exchange rate required to equalise the purchasing power of different currencies
• Interest rate parity, in finance, the notion that the differential in interest rates between two countries is equal to the differential between the forward exchange rate and the spot exchange rate
• Put–call parity, in financial mathematics, defines a relationship between the price of a European call option and a European put option
• Parity (sports), an equal playing field for all participants, regardless of their economic circumstances
• Potty parity, equalization of waiting times for males and females in restroom queues
• A tactic in reversi
• Grid parity of renewable energy
• Doctrine of parity, agricultural price controls

Parity is a mathematical term that describes the property of an integer's inclusion in one of two categories: even or odd. An integer is even if it is 'evenly divisible' by two (the old-fashioned term "evenly divisible" is now almost always shortened to " divisible") and odd if it is not even. For example, 6 is even because there is no remainder when dividing it by 2. By contrast, 3, 5, 7, 21 leave a remainder of 1 when divided by 2. Examples of even numbers include −4, 0, 8, and 1738. In particular, zero is an even number. Some examples of odd numbers are −5, 3, 9, and 73. Parity does not apply to non-integer numbers.

A formal definition of an even number is that it is an integer of the form n = 2k, where k is an integer; it can then be shown that an odd number is an integer of the form n = 2k + 1. This classification applies only to integers, i.e., non-integers like 1/2, 4.201, or infinity are neither even nor odd.

The sets of even and odd numbers can be defined as following:

• Even  = {2k : k ∈ Z}
• Odd  = {2k + 1 : k ∈ Z}

A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwise it is even. The same idea will work using any even base. In particular, a number expressed in the binary numeral system is odd if its last digit is 1 and even if its last digit is 0. In an odd base, the number is even according to the sum of its digits – it is even if and only if the sum of its digits is even.

In quantum mechanics, a parity transformation (also called parity inversion) is the flip in the sign of one spatial coordinate. In three dimensions, it is also often described by the simultaneous flip in the sign of all three spatial coordinates (a point reflection):

$$\mathbf{P}: \begin{pmatrix}x\\y\\z\end{pmatrix} \mapsto \begin{pmatrix}-x\\-y\\-z\end{pmatrix}.$$

It can also be thought of as a test for chirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image. A parity transformation on something achiral, on the other hand, can be viewed as an identity transformation. All fundamental interactions of elementary particles, with the exception of the weak interaction, are symmetric under parity. The weak interaction is chiral and thus provides a means for probing chirality in physics. In interactions that are symmetric under parity, such as electromagnetism in atomic and molecular physics, parity serves as a powerful controlling principle underlying quantum transitions.

A matrix representation of P (in any number of dimensions) has determinant equal to −1, and hence is distinct from a rotation, which has a determinant equal to 1. In a two-dimensional plane, a simultaneous flip of all coordinates in sign is not a parity transformation; it is the same as a 180°- rotation.

In sports, parity is when participating teams have roughly equivalent levels of talent. In such a league, the "best" team is not significantly better than the "worst" team. This leads to more competitive contests where the winner cannot be easily predicted in advance. The opposite condition, which could be considered "disparity" between teams, is a condition where the elite teams are so much more talented that the lesser teams are hopelessly outmatched.

Different major governing organizations attempt to achieve parity in different ways. For example, the NFL in America has established the shared revenue plan, in which all teams equally benefit from television revenue and sales of NFL franchised goods.

Many consider the NFL to be the most "fair" or competitive league, with many different teams having a chance to win each year. In the NFL, complete parity would be a state where on any given Sunday, any given team can win any given game. The illusion of parity in the NFL may be somewhat of a misconception, given that several teams such as the New England Patriots, Pittsburgh Steelers, Indianapolis Colts, and Philadelphia Eagles have appeared in the playoffs in almost all of the past ten years, while a team such as the Buffalo Bills has a playoff drought that is currently over a decade long. At the same time, you often hear people say "the same teams win every year" when speaking about baseball, but in reality 27 of the 30 teams have made the playoffs since 2008, and all thirty have made it since 2001. Then again, others would say that statistically you could expect some of that variation even in a parity league. Just the same way that you flip a coin ten times in a row, sometimes heads will come up ten times, doesn't mean it's not a fair coin. The most important thing to remember is that a franchise can be struggling and the reason for it can be due to the team's ineptitude when it comes evaluating talent, coaching strategies, developing players, having a good organizational structure, and overall team and player operations.

An example of disparity in sports is Portuguese Liga, the top-flight professional football (soccer) league in Portugal, where three clubs have accounted for 75 of the 77 championships in league history.

Salary cap limits set a maximum amount of money that may be spent on athletes' contracts. These limits exist to different extents in several other leagues as well. For example, Major League Baseball in America does not have a cap, but charges a luxury tax beyond a certain level.