Supremum & Infimum | Property | Real Analysis | Greatest lower bound | Least upper bound | Msc | Bsc

Supremum & Infimum | Properties of Supremum and Infimum | Real Analysis | Math Tutorials. --------Supremum and Infimum | Definition-----------    • Real analysis || Supremum and infimum || M...   c greater than 0 (i)Sup(cA)=cSup(A) (ii)Inf(cA)=cInf(A) c less than 0 (i) Sup(cA)=cInf(A) (ii)Inf(cA)=cSup(A) Supremum & Infimum are unique S is a bounded set then subset T of S is also Bounded. S is a non empty bounded subset of R and T is subset of S then Sup(T) is less than equal to Sup (S) S is a non empty bounded subset of R and T is subset of S then Inf(S) is less than equal to Inf(T) helpful for Msc | BSC | NET | NBHM | LPU | DU | IIT JAM | TIFR | ISI | BHU | BSc(H), CSIR NET Students. Topics Covered in playlist Real Analysis: Definition of Neighbourhood of a point. Definition of Open set. infinite intersection of open sets need not to be open Union of two NBDS is NBD Intersection of NBDS is NBD Superset of a NBD is also a NBD Every Open interval (a,b) is neighbourhood of each of its points. Closed interval is neighbourhood of each point except end points. real numbers is NBD of each real number Rational numbers set is not the neighbourhood of any of its points. Metric space | Distance Function | Example Metric space : Definition and Axioms Real Analysis : Introduction and Intervals Union of countable sets is countable Finite,infinite,equivalent,denumerable,countable sets Infinite subset of countable set is countable Field,Ordered Field,complete Ordered Field Set of Integers is Countable Supremum and infimum Set is countably infinite iff it can be written in the form distinct elements Continuum Hypothesis Cartesian product of two countable sets is Countable Set of Rational numbers is Countable -------------------------Thanks for Watching------------------------------------ Definition of metric Space Examples of metric space Open and Closed sets Topology and convergence Types of metric spaces Complete Spaces Bounded and complete bounded spaces Compact spaces Locally compact and proper spaces connectedness Separable spaces Pointed Metric spaces Types of maps between metric spaces continuous maps uniformly continuous maps Lipschitz-continuous maps and contractions isometries Quasi-isometries notions of metric space equivalence Topological properties Distance between points and sets Hausdorff distance and Gromov metric Product metric spaces Continuity of distance Quotient metric spaces Generalizations of metric spaces Metric spaces as enriched categories Supremum and infimum of sets sup and inf. value least upper bound and greatest lower bound. l.u.b. and g.l.b. this concept will be helpful for the further study of real analysis. Real analysis intro and intervals complete knowledge for bounded and unbounded intervals. LPU distance MA maths. LPU msc. maths Msc maths Ma maths Bsc maths Basic Topology Topology mathematics topology maths Topology optimization Topology lecture Topology and types Topology axioms Real analysis for BA maths Real analysis for MA Maths Real analysis for Msc. Maths Real analysis study material Real analysis books Real Analysis notes Real Analysis Basic Concept Real analysis topics Real analysis course Real analysis applications Real analysis lacture notes Real analysis proofs Real analysis text book Real analysis MIT open course LPU MA maths sylalbus LPU ma maths study material LPU MA maths solution LPU ma maths 1st year LPU MA maths books LPU MA maths sample questions LPU distance education. LPU MA Math LPU msc. maths LPU msc. math lovely professional univesity MA maths sylalbus lovely professional univesity ma maths study material lovely professional univesity MA maths solution lovely professional univesity ma maths 1st year lovely professional univesity MA maths books lovely professional univesity MA maths sample questions lovely professional univesity distance education. lovely professional univesity MA Math lovely professional univesity msc. maths lovely professional univesity msc. math Ma maths real analysis nptel real analysis mit real analysis iit jam real analysis in tamil real analysis upsc real analysis mathematics real analysis real analysis axioms real analysis book real analysis bsc maths part 2 real analysis bsc maths in hindi real analysis b tech maths bounded intervals on the real number line bounded and unbounded intervals Denumerable union of Denumerable set is Denumerable Denumerable union of Denumerable sets is Denumerable union of Denumerable sets is Denumerable a Denumerable union of Denumerable sets is Denumerable a countable union of countable sets is countable discrete math countable sets and uncountable sets countable and uncountable sets in discrete mathematics what is countable and uncountable sets finite sets and infinite sets finite sets meaning finite sets definition examples of finite sets(mathematics)