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The substitution instance tσ of a ground substitution is a ground term if all of t ' s variables are in σ ' s domain, i.e. if vars(t) ⊆ dom(σ). A substitution σ is called a linear substitution if tσ is a linear term for some (and hence every) linear term t containing precisely the variables of σ ' s domain, i.e. with vars(t) = dom(σ).
A frequently occurring case is a double covering group, a topological double cover in which H has index 2 in G; examples include the spin groups, pin groups, and metaplectic groups. Roughly explained, saying that for example the metaplectic group Mp 2 n is a double cover of the symplectic group Sp 2 n means that there are always two elements in ...
Substitution, written M[x := N], is the process of replacing all free occurrences of the variable x in the expression M with expression N. Substitution on terms of the lambda calculus is defined by recursion on the structure of terms, as follows (note: x and y are only variables while M and N are any lambda expression): x[x := N] = N
A double cover may also be used to refer to non-topological group extensions of index two, for instance extensions of finite groups. Doubling space, a possible property of a metric space. Cycle double cover, a collection of cycles in a graph that together include each edge twice. The cycle double cover conjecture is the unproven assertion that ...
Change of variables is an operation that is related to substitution. However these are different operations, as can be seen when considering differentiation or integration (integration by substitution). A very simple example of a useful variable change can be seen in the problem of finding the roots of the sixth-degree polynomial:
The epsilon operator and epsilon substitution method are typically applied to a first-order predicate calculus, followed by a demonstration of consistency. The epsilon-extended calculus is further extended and generalized to cover those mathematical objects, classes, and categories for which there is a desire to show consistency, building on ...
Term vs. whole life insurance. With term life insurance, the policyholder chooses a period during which their policy is active — usually somewhere between 10 and 30 years. The policyholder pays ...
The substitution is described in most integral calculus textbooks since the late 19th century, usually without any special name. [5] It is known in Russia as the universal trigonometric substitution, [6] and also known by variant names such as half-tangent substitution or half-angle substitution.