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Relation concatenation

Set

context RRel(X,U)
context SRel(V,Y)
definiendum x,ySR
postulate m. x,mRm,yS

Discussion

Concatenations/compositions are associative.

A mayority of uses of the relation concatenation is when the relation is functional, i.e. one composes functions alla

g:XY,  f:YZ

then

fg:XZ

(fg)(x):=f(g(x))

Notation

If f:XY and g:YZ are functions, we'll often denote fg by fg. This convenient notation will also be used in more elaborate cases. For example, if by f(x) we done the values of a function f:XR and || is the function which takes a real to its absolute value, then |f| will denote the name of the function with values |f(x)|.

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