- Видео 40
- Просмотров 5 681
Biswajit Biswas
Добавлен 11 июл 2020
Some concepts about mathematics
Quotient Group
Quotient Group: Let H be a normal subgroup of a group G. Then the set of all distinct cosets of H in G forms a group with respect to the binary operation * defined by, aH*bH=abH ; for all a,b∈G .
Просмотров: 240
Видео
Let H be a subgroup of G. Then H is normal in G iff for h∈H and x∈G ⇒ xhx⁻¹∈H .
Просмотров 44Месяц назад
Let H be a subgroup of G. Then H is normal in G iff for h∈H and x∈G ⇒ xhx⁻¹∈H .
The set of all distinct left cosets and right cosets have the same cardinality.
Просмотров 24Месяц назад
Let H be a subgroup of a group G.Then the set of all distinct left cosets of H in G and the set of all distinct right cosets of H in G have the same cardinality.
G be a cyclic group of order n.Then for every+ve divisor m of n,G has a unique subgroup H of order m
Просмотров 79Месяц назад
Let G be a finite cyclic group of order n . Then for every positive divisor m of n , G has a unique subgroup H of order m. Converse of Lagrange's Theorem hold for a cyclic group, since a cyclic group is commutative and a commutative group satisfies Converse of Lagrange's Theorem. For every divisor of order of a cyclic group there exists a unique subgroup of that order. This is an important theo...
For every positive integer n , ∑φ(d)=n ; where the sum being taken for all positive divisors d of n
Просмотров 30Месяц назад
Gauss Theorem: For every positive integer n , ∑ φ(d)=n ; where the sum being taken for all positive divisors d of n. Actually here we divide a cyclic group with the equivalence relation 𝔓 such that a𝔓b iff o(a)=o(b). Then we get that every class contains the generators of the subgroup of particular order. We have the result that every equivalence relation partition a set. So here the above equi...
Lagrange's Theorem:The order of every subgroups of a finite group G, is a divisor of the order of G
Просмотров 23Месяц назад
Lagrange's Theorem: The order of every subgroups of a finite group G, is a divisor of the order of G.
Every subgroups of a cyclic group is cyclic.
Просмотров 43Месяц назад
Every subgroups of a cyclic group is cyclic.
![A function f which is continuous on a closed interval [a,b] is also uniformly continuous on [a,b]](/img/1.gif)
A function f which is continuous on a closed interval [a,b] is also uniformly continuous on [a,b]
Просмотров 2404 месяца назад
A function f which is continuous on a closed interval [a,b] is also uniformly continuous on [a,b] . Music credit goes to:: Artist: Jarico Song: Island [NCS BEST OF] Download/Stream: audiograb.com/1Mm2M6Qccq
Function f is continuous on [a,b] and f(a) ≠f(b) , then it assumes every value between f(a) and f(b)
Просмотров 274 месяца назад
Music credit goes to:: Artist: Jarico Song: Island [NCS BEST OF] Download/Stream: audiograb.com/1Mm2M6Qccq
f is continuous on [a,b] and f(a).f(b) is ( -ve) then ∃ at least one point α∈(a,b) such that f(α)=0
Просмотров 224 месяца назад
If a function f is continuous on a closed interval [a,b] and f (a) , f(b) are of opposite signs i.e. f(a).f(b) less than 0 , then ∃ at least one point α ∈ (a,b) such that f(α)=0. Music credit goes to:: Artist: Jarico Song: Island [NCS BEST OF] Download/Stream: audiograb.com/1Mm2M6Qccq
An important property of continuous functions defined on a closed interval [a,b] .
Просмотров 1525 месяцев назад
If a function f is continuous at an interior point c of an interval [a,b] and f(c)≠ 0 , then ∃ a δ greater than 0 such that f(x) has the same sign as f(c) , for every x ∈ (c-δ,c δ) . Music credit goes to:: Artist: Jarico Song: Island [NCS BEST OF] Download/Stream: audiograb.com/1Mm2M6Qccq
f is continuous on a closed interval [a,b] , then it attains it's bounds at least once in [a,b] .
Просмотров 305 месяцев назад
If a function f is continuous on a closed interval [a,b] , then it attains it's bounds at least once in [a,b] .
If a function f is continuous on a closed interval [a,b] , then it is bounded therein.
Просмотров 255 месяцев назад
If a function f is continuous on a closed interval [a,b] , then it is bounded therein.
f on I is continuous at a point c ∈ I iff for every sequence {cₙ} in I , cₙ→c , we have, f(cₙ)→f(c)
Просмотров 355 месяцев назад
A function f defined on an interval I is continuous at a point c ∈ I iff for every sequence {cₙ} in I , cₙ→c , we have , f(cₙ)→f(c)
Proof of Cauchy's Criterion for finite limits
Просмотров 405 месяцев назад
Proof of Cauchy's Criterion for finite limits
The derived set S' of a bounded infinite set S (⊂R) has the smallest and the greatest members.
Просмотров 4247 месяцев назад
The derived set S' of a bounded infinite set S (⊂R) has the smallest and the greatest members.
The derived set of a bounded set is bounded.
Просмотров 387 месяцев назад
The derived set of a bounded set is bounded.
The supremum(infimum) of a bounded nonempty set S(⊂ R),when not a member of S,is a limit point of S
Просмотров 437 месяцев назад
The supremum(infimum) of a bounded nonempty set S(⊂ R),when not a member of S,is a limit point of S
A closed set either contains an interval or else is nowhere dense.
Просмотров 518 месяцев назад
A closed set either contains an interval or else is nowhere dense.
Union of an arbitrary family of open sets is open and intersection for closed sets is closed .
Просмотров 238 месяцев назад
Union of an arbitrary family of open sets is open and intersection for closed sets is closed .
A set is closed iff its complement is open.
Просмотров 518 месяцев назад
A set is closed iff its complement is open.
Bolzano-Weierstrass Theorem: Every infinite bounded set has a limit point.
Просмотров 288 месяцев назад
Bolzano-Weierstrass Theorem: Every infinite bounded set has a limit point.
Interior of S i.e. int(S)=S⁰ - is an open set , moreover it is the largest open set contained in S.
Просмотров 339 месяцев назад
Interior of S i.e. int(S)=S⁰ - is an open set , moreover it is the largest open set contained in S.
Every open interval (a , b) contains a rational number .
Просмотров 989 месяцев назад
Every open interval (a , b) contains a rational number .
Dedekind's property and Order-Completeness property in R are equivalent.
Просмотров 6510 месяцев назад
Dedekind's property and Order-Completeness property in R are equivalent.
Show that set of all rational numbers is not order-complete .
Просмотров 82Год назад
Show that set of all rational numbers is not order-complete .
Thank you guys for your extraordinary support 🖤 There are still many achievements to break . Keep learning with our team 🖤
THANK YOU GUYS FOR YOUR AMAZING SUPPORT, KEEP LEARNING 🖤
Thank You everyone for such unconditional love 💝❤
Before going to Corollary I have to mention that : Thus for all ξ ∈ S´, m≤ξ≤ M , so S´⊂[m,M].
There is a mistake : " S' has no limit point greater than it's upper bound M " will be replaced by "S has no limit point greater than it's upper bound M " . Sorry for this.
bro forgot to use his own voiceover
For Archimedean Property and it's Corollaries , watch the video : ruclips.net/video/ZocAz_HlVEE/видео.htmlsi=M34b-a7m9PvjoAbC
i dont think eqn on linr OB is correct
Yes , you are right. The equation of OB will be : x/1=y/(1/2)=z/0 . Thank You so much.
Please note that : Euclid's lemma - If a prime p divides the product ab of two integers a and b, then p must divide at least one of those integers a or b.
Thanks you so much sir
dada tomar number ta debe
8509720860
Tnx