set6 (version 0.2.4)

setunion: Union of Sets

Description

Returns the union of objects inheriting from class Set.

Usage

setunion(..., simplify = TRUE)
# S3 method for Set
+(x, y)
# S3 method for Set
|(x, y)

Arguments

...

Sets

simplify

logical, if TRUE (default) returns the result in its simplest (unwrapped) form, usually a Set, otherwise a UnionSet.

x, y

Set

Value

An object inheriting from Set containing the union of supplied sets.

Details

The union of \(N\) sets, \(X1, ..., XN\), is defined as the set of elements that exist in one or more sets, $$U = \{x : x \epsilon X1 \quad or \quad x \epsilon X2 \quad or \quad...\quad or \quad x \epsilon XN\}$$

The union of multiple ConditionalSets is given by combining their defining functions by an 'or', |, operator. See examples.

The union of fuzzy and crisp sets first coerces fuzzy sets to crisp sets by finding their support.

See Also

Other operators: powerset(), setcomplement(), setintersect(), setpower(), setproduct(), setsymdiff()

Examples

# NOT RUN {
# union of Sets

Set$new(-2:4) + Set$new(2:5)
setunion(Set$new(1, 4, "a"), Set$new("a", 6))
Set$new(1, 2) + Set$new("a", 1i) + Set$new(9)

# union of intervals

Interval$new(1, 10) + Interval$new(5, 15) + Interval$new(20, 30)
Interval$new(1, 2, type = "()") + Interval$new(2, 3, type = "(]")
Interval$new(1, 5, class = "integer") +
  Interval$new(2, 7, class = "integer")

# union of mixed types

Set$new(1:10) + Interval$new(5, 15)
Set$new(1:10) + Interval$new(5, 15, class = "integer")
Set$new(5, 7) | Tuple$new(6, 8, 7)

# union of FuzzySet
FuzzySet$new(1, 0.1, 2, 0.5) + Set$new(2:5)

# union of conditional sets

ConditionalSet$new(function(x, y) x >= y) +
  ConditionalSet$new(function(x, y) x == y) +
  ConditionalSet$new(function(x) x == 2)

# union of special sets
PosReals$new() + NegReals$new()
Set$new(-Inf, Inf) + Reals$new()
# }