Sub sequence of a Sequence | Definition | Theorem of sub sequence | Real Analysis | Subsequence

Sub sequence | Sub sequence of a sequence | Definition of Subsequence | Theorem of Subsequence | Sequence and series | Real analysis | math tutorials | Classes By Cheena Banga.
A Sequence converges to x then its sub sequence also converges to x.
if a sequence converges then its subsequences converge
Subsequence of a convergent sequence is convergent.
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***sequence and series | Real analysis | Real sequence | definition | Theorems***
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***Real Analysis playlist***
• Real Analysis
useful for Msc | BSC | NET | NBHM | LPU | DU | IIT JAM | TIFR
Other topics covered in playlist:
Algebraic Properties of Limits
Algebra of limit of sequence
Properties of limit
limit laws of sequence
sandwich theorem
squeeze theorem
Sequence and series
real sequence
range of sequence
constant sequence
uniqueness theorem
Sequences in metric space
limit of sequence
Convergent sequence
Every connected subset of R is an interval
The Real line R is connected
Every interval is connected
In R, intervals and only intervals are connected.
A subset E of R is connected iff E is an interval
compactness in Real Analysis
Connectedness in Real Analysis
Compactness in topology
Connectedness in topology
compactness
connectedness
theorems of compactness
theorems of connectedness
Heine-Borel theorem
Closed Set | definition | theorems
set is closed iff its complement is open
Bolzano weierstrass theorem : Every infinite bounded subset of R has a limit point.
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
Keep Watching
Math Tutorials
Classes by Cheena Banga
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
Compactness in Real analysis
compactness in metric space
compactness in topology
compactness and connectedness in real analysis
compactness and connectedness
compactness in topological space
Connectedness in Real analysis
connectedness in metric space
connectedness in topology
connectedness in topological space
Theorems on connectedness
theorems on compactness
Theorems of connectedness
theorems of compactness

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[@Mano_Vikas]

Wonderful lecture. Thanks Mam.

[@satyaa5480]

Mam numerical analysis ke liye video banaye please🙏🙏

[@OMGMaths]

After completion of Real analysis

[@Zftrenz]

God bless you

[@OMGMaths]

Glad it was helpful 😊
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[@yashiashi4423]

Konsi book ko follow kr rhe ho aap name btayi

[@GurnamSingh-vn4dm]

Mam aap konsi book follow kar rhe ho proof ke liye?

[@OMGMaths]

th-cam.com/users/postUgzGiqnrFcvKGA4AmSN4AaABCQ

[@bikashsharma2702]

Mam voh ni and nk samjh nhi aaya .voh thora diagram aalag bana dete subsequence ka or phir btate ka toh clear ho jata .

[@satyaa5480]

Good night mam

[@OMGMaths]

Very Good night