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The usual order relation on the real numbers is antisymmetric: if for two real numbers and both inequalities and hold, then and must be equal. Similarly, the subset order on the subsets of any given set is antisymmetric: given two sets and if every element in also is in and every element in is also in then and must contain all the same elements ...
The double turnstile is a binary relation. It has several different meanings in different contexts: This usage is closely related to the single-barred turnstile symbol which denotes syntactic consequence. This is typically done inductively along with restricting the range of a variable assignment, a function mapping each variable symbol to a ...
If the constant term is 0, then it will conventionally be omitted when the quadratic is written out. Any polynomial written in standard form has a unique constant term, which can be considered a coefficient of . In particular, the constant term will always be the lowest degree term of the polynomial. This also applies to multivariate polynomials.
Weak solution. In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate ...
Half-space (geometry) In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space. If the space is two-dimensional, then a half-space is called a half-plane (open or closed). A half-space in a one-dimensional space is called a half-line or ray. More generally, a half-space is either of ...
A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. [1] In a sense, these are nullary (i.e. 0- arity) predicates.
An intransitive or non-transitive game is a zero-sum game in which pairwise competitions between the strategies contain a cycle. If strategy A beats strategy B, B beats C, and C beats A, then the binary relation "to beat" is intransitive, since transitivity would require that A beat C. The terms "transitive game" or "intransitive game" are not ...
where E is the expected value operator. Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If Y always takes on the same values as X, we have the covariance of a variable with itself (i.e. ), which is called the variance and is more commonly denoted as the square of the ...