Calculates and returns the powerset of a Set.

powerset(x, simplify = FALSE)

Arguments

x

Set

simplify

logical, if TRUE then tries to simplify the result to a Set otherwise creates an object of class PowersetSet.

Value

Set

Details

A powerset of a set, S, is defined as the set of all subsets of S, including S itself and the empty set.

See also

Examples

# simplify = FALSE is default powerset(Set$new(1, 2))
#> ℘({1, 2})
powerset(Set$new(1, 2), simplify = TRUE)
#> {∅, {1}, {2}, {1, 2}}
# powerset of intervals powerset(Interval$new())
#> ℘([-∞,+∞])
# powerset of powersets powerset(powerset(Reals$new()))
#> ℘(℘(ℝ))
powerset(powerset(Reals$new()))$properties$cardinality
#> [1] "Beth3"