## Sets

R6 classes and methods inheriting from class Set

Set

Mathematical Set

Tuple

Mathematical Tuple

Interval

Mathematical Finite or Infinite Interval

FuzzySet

Mathematical Fuzzy Set

FuzzyTuple

Mathematical Fuzzy Tuple

ConditionalSet

Mathematical Set of Conditions

## Special Sets

Universal

Mathematical Universal Set

Logicals

Set of Logicals

Naturals

Set of Natural Numbers

PosNaturals

Set of Positive Natural Numbers

Integers

Set of Integers

PosIntegers

Set of Positive Integers

NegIntegers

Set of Negative Integers

Rationals

Set of Rational Numbers

PosRationals

Set of Positive Rational Numbers

NegRationals

Set of Negative Rational Numbers

Reals

Set of Real Numbers

PosReals

Set of Positive Real Numbers

NegReals

Set of Negative Real Numbers

ExtendedReals

Set of Extended Real Numbers

Complex

Set of Complex Numbers

listSpecialSets()

Lists Implemented R6 Special Sets

## Set Operations

Classes and operators for combining sets

UnionSet

Set of Unions

setunion() +(<Set>) |(<Set>)

Union of Sets

ComplementSet

Set of Complements

setcomplement() -(<Set>)

Complement of Two Sets

setsymdiff() %-%

Symmetric Difference of Two Sets

powerset()

Calculate a Set's Powerset

PowersetSet

Set of Powersets

ProductSet

Set of Products

setproduct() *(<Set>)

Cartesian Product of Sets

ExponentSet

Set of Exponentiations

setpower() ^(<Set>)

Power of a Set

setintersect() &(<Set>)

Intersection of Two Sets

## Assertions

Validation checks for Sets

testClosed() checkClosed() assertClosed()

assert/check/test/Closed

testClosedAbove() checkClosedAbove() assertClosedAbove()

assert/check/test/ClosedAbove

testClosedBelow() checkClosedBelow() assertClosedBelow()

assert/check/test/ClosedBelow

testConditionalSet() checkConditionalSet() assertConditionalSet()

assert/check/test/ConditionalSet

testContains() checkContains() assertContains()

assert/check/test/Contains

testCountablyFinite() checkCountablyFinite() assertCountablyFinite()

assert/check/test/CountablyFinite

testCrisp() checkCrisp() assertCrisp()

assert/check/test/Crisp

testEmpty() checkEmpty() assertEmpty()

assert/check/test/Empty

testFinite() checkFinite() assertFinite()

assert/check/test/Finite

testFuzzy() checkFuzzy() assertFuzzy()

assert/check/test/Fuzzy

testFuzzyMultiset() checkFuzzyMultiset() assertFuzzyMultiset()

assert/check/test/FuzzyMultiset

testFuzzySet() checkFuzzySet() assertFuzzySet()

assert/check/test/FuzzySet

testFuzzyTuple() checkFuzzyTuple() assertFuzzyTuple()

assert/check/test/FuzzyTuple

testInterval() checkInterval() assertInterval()

assert/check/test/Interval

testMultiset() checkMultiset() assertMultiset()

assert/check/test/Multiset

testSet() checkSet() assertSet()

assert/check/test/Set

testSetList() checkSetList() assertSetList()

assert/check/test/SetList

testSubset() checkSubset() assertSubset()

assert/check/test/Subset

testTuple() checkTuple() assertTuple()

assert/check/test/Tuple

## Coercions

S3 methods for coercing objects to Sets

as.FuzzySet() as.FuzzyTuple() as.FuzzyMultiset()

Coercion to R6 FuzzySet/FuzzyTuple

as.Interval()

Coercion to R6 Interval

as.Set() as.Tuple() as.Multiset()

Coercion to R6 Set/Tuple

testClosed() checkClosed() assertClosed()

assert/check/test/Closed

testClosedAbove() checkClosedAbove() assertClosedAbove()

assert/check/test/ClosedAbove

testClosedBelow() checkClosedBelow() assertClosedBelow()

assert/check/test/ClosedBelow

testConditionalSet() checkConditionalSet() assertConditionalSet()

assert/check/test/ConditionalSet

testContains() checkContains() assertContains()

assert/check/test/Contains

testCountablyFinite() checkCountablyFinite() assertCountablyFinite()

assert/check/test/CountablyFinite

testCrisp() checkCrisp() assertCrisp()

assert/check/test/Crisp

testEmpty() checkEmpty() assertEmpty()

assert/check/test/Empty

testFinite() checkFinite() assertFinite()

assert/check/test/Finite

testFuzzy() checkFuzzy() assertFuzzy()

assert/check/test/Fuzzy

testFuzzyMultiset() checkFuzzyMultiset() assertFuzzyMultiset()

assert/check/test/FuzzyMultiset

testFuzzySet() checkFuzzySet() assertFuzzySet()

assert/check/test/FuzzySet

testFuzzyTuple() checkFuzzyTuple() assertFuzzyTuple()

assert/check/test/FuzzyTuple

testInterval() checkInterval() assertInterval()

assert/check/test/Interval

testMultiset() checkMultiset() assertMultiset()

assert/check/test/Multiset

testSet() checkSet() assertSet()

assert/check/test/Set

testSetList() checkSetList() assertSetList()

assert/check/test/SetList

testSubset() checkSubset() assertSubset()

assert/check/test/Subset

testTuple() checkTuple() assertTuple()

assert/check/test/Tuple

## Miscellaneous Functions

useUnicode()

Get/Set Unicode Printing Method

set6News()

Show set6 NEWS.md File