faunjdikpe

valsi

faunjdikpe

type

fu'ivla

creator

krtisfranks

time entered

Mon May 16 17:15:40 2016  

English

Definition #68660 - Preferred

 

definition

x₁ (function) is the restriction of function x₂ to domain set x₃

notes

x₃ should normally be a (strict) subset of the domain set of x₁; however, for generality, any set is allowed, but x₁ will be undefined everywhere except on/in the intersection of x₃ with the domain set of x₂. Outside of x₃, x₁ is undefined, even if x₂ is. In/on x₃, x₁ and x₂ are identically equal everywhere. x₂ is a specific extension of x₁. For the sense of restriction in which, instead of being undefined outside of x₃, x₁ is identically equal to the zero element of the space on the set exclusion of the domain of x₂ lacking x₃ (and which is undefined everywhere not in the domain set of x₂), try to use a product of a zdeltakronekre function with x₂, which will be defined on the intersection of their two domain sets and will identically be 0 or x₂ as specified. Be careful, concerning x₃, when the domain set of x₂ is the Cartesian product (pi'u) of sets; for example, R is not a subset of R², even if it is isomorphic to one (actually, uncountably infinitely many in this case).

gloss words

• function restriction
• restriction ; of a function to a subset of its domain

created by

krtisfranks

vote information

1

time

Mon May 16 17:15:40 2016

Examples

---