set theory
Math of groups
Set theory is the branch of mathematics concerned with sets—collections of distinct objects considered as wholes.
It provides the foundational language for nearly all modern mathematics, defining concepts like membership, union, intersection, and cardinality.
Set theory shows that some infinities are larger than others.
Basic set theory appears in school math; advanced set theory explores the logical foundations of mathematics itself.
Having definite bounds
- infiniteHaving no bounds
- countableAble to be tallied
- uncountableNot able to enumerate
- cardinalitySize of a set
continuum · continuum hypothesis · Cantor · ordinal · cardinal numbers · injection · one-to-one · onto
Set intersection illustration
- overlappingCovering part of another
- circlesEquidistant curves from centers
- regionIndefinite bounded area
- shadingDepicting light and darkness
visual representation · inclusion · exclusion · disjoint · complement · union · classification
Joining into one
- complementWhat makes complete
- differenceWay things contrast
- De Morgan's lawsLogical negation distribution rules
- distributiveConcerning fair division
commutative · associative · identity · partition · combination · merge
Self-evident starting principle
- elementBasic substance or factor
- membershipState of belonging
- complementWhat makes complete
- well-definedHaving clear boundaries
axiomatic · specification · regularity · pairing · comprehension · belonging · collection · class
Statement expressing a judgment
- predicateSentence's non-subject portion
- quantifierWord expressing amount
- existentialRelating to existence itself
- universalAffecting all equally
negation · conjunction · disjunction · implication · proof · theorem · contradiction · truth value
Purpose or duty
- mappingDiagram of correspondences
- relationConnection or kin
- equivalenceState of being equal
- domainArea of control
range · ordered pair · reflexive · symmetric · transitive · antisymmetric · image · correspondence
finite
Having definite bounds
- infiniteHaving no bounds
- countableAble to be tallied
- uncountableNot able to enumerate
cardinality · continuum · continuum hypothesis · Cantor · ordinal · cardinal numbers · injection · one-to-one · onto · Cantor's theorem
Venn diagram
Set intersection illustration
- overlappingCovering part of another
- circlesEquidistant curves from centers
- regionIndefinite bounded area
shading · visual representation · inclusion · exclusion · disjoint · complement · union · classification
union
Joining into one
- complementWhat makes complete
- differenceWay things contrast
- De Morgan's lawsLogical negation distribution rules
distributive · commutative · associative · identity · partition · combination · merge
axiom
Self-evident starting principle
- elementBasic substance or factor
- membershipState of belonging
- complementWhat makes complete
well-defined · axiomatic · specification · regularity · pairing · comprehension · belonging · collection · class
proposition
Statement expressing a judgment
- predicateSentence's non-subject portion
- quantifierWord expressing amount
- existentialRelating to existence itself
universal · negation · conjunction · disjunction · implication · proof · theorem · contradiction · truth value · necessary
function
Purpose or duty
- mappingDiagram of correspondences
- relationConnection or kin
- equivalenceState of being equal
domain · range · ordered pair · reflexive · symmetric · transitive · antisymmetric · image · correspondence · inverse
- mathaddition, subtraction, multiplication, division, algebra
- mathematicsalgebra, arithmetic, calculus, geometry, number
- academic fieldsmathematics, biology, chemistry, physics, history
- exact sciencesmathematics, physics, chemistry, math, algebra
- math resourcesmath tutorials, linear algebra, differential equations, worked examples, practice problems
- scientific theoriesevolution, general relativity, relativity, plate tectonics, special relativity
set theoryarithmetic
Mathematics of basic operations
applied mathematics · computation · number theory · number crunching · counting