Academic Maths

Tagged with: absolute value • absolute value of a real number • addition • additive inverse • additive inverses • associative • associativity • associativity of addition • associativity of multiplication • associativity of the addition • associativity of the multiplication • axioms of addition • axioms of multiplication • bounded interval • bounded set • bounded subset • bounded subset of real numbers • bounded subset of the real numbers • bounded subsets of real numbers • bounded subsets of the real numbers • closed interval • commutativity • commutativity of addition • commutativity of multiplication • commutativity of the addition • commutativity of the multiplication • completeness of the real numbers • construction of real numbers • construction of the real numbers • criteria of supremum and infimum • criterion of supremum and infimum • distance between two real numbers • distributivity of multiplication over addition • entending of the real numbers • existence of additive inverse • existence of infimum • existence of multiplicative inverse • existence of supremum • existence of supremum and infimum • existence of supremum and infimum in reals • existence of supremum and infimum in the real numbers • extended real number line • extended real number system • extended real numbers • greatest lower bound • greatest lower bound property • identity element • infimum • infimum in reals • infimum of a set • infinity • interval • interval lied real numbers • interval lied reals • interval with the endpoint a and b • least upper bound • least upper bound property • left closed left open interval • left open right closed interval • length of an interval • lower bound • lower bounds • maximum • maximum element • maximum element of a set • maximum element of a subset • measure of an interval • minimum • minimum element • minimum element a set • minimum element a subset • modulus • modulus of a real number • multiplication • multiplication of negative and negative is positive • multiplication of negative number and negative number is positive number • multiplication of positive and negative is negative • multiplication of positive and positive is positive • multiplication of positive number and negative number is negative number • multiplication of positive number and positive number is positive number • multiplicative inverse • multiplicative inverses • negative • negative infinity • negative real numbers • open interval • operation addition • operation multiplication • order • order of real numbers • ordering of the real numbers • positive • positive infinity • positive real numbers • proof of infimum • proof of reverse triangle inequality • proof of supremum • proof of triangle inequality • properties of modulus • properties of the absolute value • properties of the extended real numbers • real number • real numbers • reverse triangle inequality • sets supremum infimum • size of an interval • supremum • supremum and infimum in reals • supremum in reals • supremum infimum • supremum of a set • the axiomatic structure of the real numbers • the axioms of the addition • the axioms of the multiplication • the identity of multiplication • the identity of the multiplication • the negative real numbers • the order • the positive real numbers • the real numbers • the set of lower bound of a set • the set of real numbers • the set of real numbers is associative • the set of real numbers is complete • the set of the real numbers • the set of upper bound of a set • the zero of addition • the zero of the addition • triangle inequality • unbounded interval • uniqueness of identity element • uniqueness of zero • upper bound • upper bounds • width of an interval • zero 

Tagged with: bijection • bijections • bijective • bijective function • bijective functions • characteristic function • codomain • codomain of a function • composition • composition of functions • composition of two functions • constant function • domain • domain of a function • example of bijection • example of bijections • example of bijective function • example of bijective functions • example of functions • example of one to one correspondence • example of one to one corresponding • extension • function • functions • group of functions • identity • identity function • image • image of a function • image of a set • image of an element • images • inclusion • inclusion function • injection • injections • injective • injective and surjective • injective function • injective functions • inverse • inverse function • inverse image • inverse image of a set • inverse of a function • invertible • left and right inverses • left inverse • map • mapping • mappings • maps • one to one • one to one correspondence • one to one corresponding • one to one function • one to one functions • onto • onto function • onto functions • preimage • preimage of a set • range • ranges • restriction • restriction and extension • right inverse • sujective function • surjection • surjective functions 

Tagged with: equivalence • equivalence class • equivalence classes • equivalence relation • equivalence relations • partition • partition of a set • quotient set • reflexive • reflexive symmetric transitive • relation • relation in math • relations • relations in math • representative class • representative classes • symmetric • transitive 

Tagged with: antisymmetric • bounded • bounded set • bounded sets • chain • chain in a set • chain in set • chain of a set • completely ordered set • completely ordered sets • criteria of supremum and infimum • criterion of supremum and infimum • existence of infimum • existence of supremum • existence of supremum and infimum • existence of supremum and infimum in reals • existence of supremum and infimum in the real numbers • gcd • greatest common divisor • greatest lower bound • infimum • infimum in reals • infimum of a set • lcm • least common multiple • least upper bound • lemma of zorn • linearly ordered set • linearly ordered sets • lower bound • lower bound in set • lower bound in sets • lower bounds • maximal • maximal and minimal element • maximal and minimal elements • maximal element • maximal element of a set • maximal elements • maximal elements of a set • maximum • maximum and minimum element • maximum element • maximum element of a set • minimal • minimal element • minimal element a set • minimal elements • minimal elements a set • minimum • minimum element • minimum element a set • order • order theory • ordered • partial order relation • partial order relations • partial ordered sets • partially ordered set • problems of infimum • problems of supremum • problems of supremum and infimum • proof of infimum • proof of supremum • reflexive • reflexive antisymmetric transitive • semi order • semi ordered • semi ordered set • semi ordered sets • sets supremum infimum • supremum • supremum and infimum in reals • supremum and infimum of a set • supremum in reals • supremum infimum • supremum of a set • the supremum of a set • total order • total order relation • totally ordered set • totally ordered sets • transitive • upper bound • upper bound in set • upper bound in sets • upper bounds • well order • well ordered • well ordered set • zorn • zorn's lemma 

Tagged with: calculus • composition of relations • converse of relation • converse of relations • equivalence relation • equivalence relations • expression for relation • expression for relations • inverse of a relation • inverse of relation • inverse of relations • order relation • order relations • partial order relation • partial order relations • partial ordered set • partial ordered sets • partially ordered set • partially ordered sets • poset • relation • relation in math • relations • relations in math 

Tagged with: index • index set • index set in math • index sets • indexed set • indexed sets • indexing a set • the index set • the index set in math 

Tagged with: bertrand russell • paradox • paradox of russell • paradoxes in math • paradoxes in maths • russell • russell paradox • russell's paradox 

Tagged with: advanced maths on sets • common property • define set in math • define set in math and give example • definition of set • diffrence of sets • emptyset • examples of math universal and intersection sets • family of sets • family set of real numbers • intersection • intersection of sets • list format • math method of sets • math proposition • math proposition problems • math proposition sets • math propositions sets • math union and intersection • proof of symmetric difference properties • proofs of symmetric difference properties • proposition • propositions • set • set concept • set example • set examples • set theory • sets • sets example • sets examples • sets math • symmetric difference • symmetric difference proof • theorical math • types of set math • types of sets in math • types of sets in maths • union • union of sets • universal set • university math • venn diagram • what is a math proposition • what is a set proposition