(0 1) is uncountable|(0,1) is uncountable proof|countable uncountable sets|uncountable set proof

[@prof.lalitkumarpachori8508]

माझ्या वडिलांचे जगणे माझे आहे, परंतु माझे वडील चांगले आहेत. आपण आम्हाला शिक्षित करण्यासाठी जी मेहनत आणि प्रयत्न केले त्याबद्दल आम्ही नेहमीच आभारी आहोत मी तुमच्यासारखा गुरु मिळालो याबद्दल मी भाग्यवान होतो. प्रिय शिक्षक, मला नेहमीच पाठिंबा दिल्याबद्दल आणि माझे मार्गदर्शन केल्याबद्दल धन्यवाद. जर मला तुमचा आशीर्वाद नेहमी मिळाला असता तर मी यशस्वी झालो असतो. 😍

[@prof.lalitkumarpachori8508]

The Cantor set is an example of an uncountable set of Lebesgue measure 0 which is not of strong measure zero. Borel's conjecture states that every strong measure zero set is countable. ... A set A ⊆ R has strong measure zero if and only if A + M ≠ R for every meagre set M ⊆ R.

[@aniketpal9629]

Darunnnn sirrr. Khub sundarrrr bojhalen sir .

[@jadekan72]

Great! I didn't understand the way my teacher in the school doing this proof. But here I got hjelp! Thanks so much!

[@Kalpanadubey11]

Sir apke pdane ka trika bhut accha hai please keep it

[@generalhcross]

This is the first explanation that I was able to understand. Thank you!!

[@MdMahafuzurRahman-y3o]

Thank you so much sir..My concept is clear now..Please take love💌

[@mansafabrar6872]

Best proof for R to be uncountable. 👍

[@floatingmoose]

Thank you for making this video. It made the arguments clear and easy to understand!

[@inovexa4039]

This is excellent sir!! Much love from Sri Lanka. The best explanation I've seen so far...

[@gavinhyde2849]

Great video. Straight to the point and easy to understand.

[@devanshpandya3818]

Natural lite is good concept Yaa Ur explanation is also

[@benedictkongyir1899]

May God bless you for your work

[@devadathan6620]

easy to understand. Very useful .❤️👍

[@kousei8411]

Simple and easy explanatiion

[@reactionboy4437]

Sir,I learned many things from this lecture

[@subhopal1760]

Thnk sir....plzz sir upload vedios for csir net...

[@diejodomison4249]

Amazing video sir

[@cut143]

Sir Topology questions and answers video daliye please

[@priyanqajha4838]

Finally crystal clear

[@sridharreddy4162]

Well explanation sir

[@pradhumansinghchouhan9237]

great video

[@mathematicsmind8648]

It's simply awesome.. 🙏

[@MathematicalMinds]

Sir Please define uncountable union & countable union of sets

[@bilalmusharraf9321]

Sir plz make a complete series of important topics for IIT jam

[@soniyasharma3406]

Very beautifully explained, sir. I got it but I've a question, we have let that B, what if this assumption is wrong????? What if there doesn't exist such B. Maths is mysterious!!

[@greatisnothing]

There exist such B, just as we define it. It's Because we can proof that there is one element such as B exist that is not listed, it proves that its uncountable.

[@soniyasharma3406]

@@greatisnothing , yes. Got your point.

[@kaushalkumar-oz3eh]

Sir please upload some lecture Riemann integral 🙏🙏🙏

[@sabindragaurinteresting7126]

Watch gajendra purohit videos

[@sahayam80]

good explanation. thank you

[@Chysrh]

Nyc expl.

[@ranjithkumar-vl8mq]

Thank u sir..to teaching in english...

[@vlog_vihar]

Sir good explanation but Hindi me bolte to or achha samajh ata. Thankyou sir

[@michaelbachmann457]

very lovely explained thank you :)

[@Dream16780]

Bahut hard

[@Dream16780]

And sir..you are really a good teacher..thanks for your lecture.

[@dollykashyap4665]

thnks sir u re the best 🥰

[@indugupta6081]

Thanks Sir

[@lucienchu9649]

Sorry sir, I am pretty confused, say a11 = 7, then b1 = 8. Isn't that we can always find a number in the list such that it starts with 0.8 then bla bla bla which will ultimately match the number B?

[@saskiarymkiewicz260]

thank you, this really helped me

[@ethangrubelich1305]

KING. THANK YOU.

[@boxman_ninja0819]

Why can we not apply this proof to the set of rational numbers?

[@soniyasharma3406]

I'm so happy that i got it. I'm so bad with proofs. Any suggestions to improve it???

[@sarojghosh7916]

Any connected metric space with atleast two elements must be uncountable .

[@tit-bits6197]

Killing a mosquito with a Canon?

[@baisarinku2340]

Sir aap unacadamy app pr class kyu nhi le rhe.....??

[@monoramamandal4941]

Thank you so much ..

[@D_i_n_e_s_562]

Thanq sir...

[@ganeshmapari1576]

Like Classic girukul,like that, thanks

[@ganeshmapari1576]

Gurukul

[@RahulMapariBasicMaths]

Oh. Thank you so much brother.

[@alizach.3708]

Sir agr ic ki jaga (0,5) is uncountable prove karna hoto same aise hi hoga??

[@RahulMapariBasicMaths]

Yes

[@alizach.3708]

​@@RahulMapariBasicMaths thankss sir

[@poojaingole416]

Thank you sir...

[@radhikasavalam6696]

Thank you Sir

[@akhileshkumarojha9301]

Thank you so much sir 🙏🙏

[@mathsclub1903]

what is the condition of b1 not equal to a11

[@ieltscuecard467]

Why nonmeasurable set is uncountable????

[@AjaySingh-bk6lk]

Sir isko cator set ki help se prove kr saktay h kiya

[@ananddanodiya2324]

Thank sir

[@amandeep9930]

A countable set has measure zero. Since measure of (0,1) is 1,it must be uncountable.

[@RahulMapariBasicMaths]

Very good. But we have some examples that a set is Uncountable but measure is zero.

[@amandeep9930]

@@RahulMapariBasicMaths Yes Sir, the most well known example is Cantor Set. Sir, I watch your videos regularly. Thank You for helping us.

[@mansafabrar6872]

Could u please explain measure zero concept?

[@aniketpal9629]

I am now reading in 6th sem b.sc . And i was unable to understand the proof of this thm. untill watching the proof u provided it sir

[@IAF-Lover001]

Studying 📚✏✔

[@gandhamprasanthi7035]

Thank u sir

[@AB_K96]

Thanks you sir 😇

[@nileshgangurde4893]

aii not equal to bi Aise assumption krna hi q he Agar aise assumption nhi krenge to countable ho jayega na

[@ايمانعلي-ظ6ت]

Please help me in the theorem (0,1) is countable

[@RahulMapariBasicMaths]

(0,1) is uncomfortable.

[@ايمانعلي-ظ6ت]

@@RahulMapariBasicMaths I have solution or the proof that Is not countable

[@osmaniavenky4874]

Super sir

[@danielzhu4487]

Preciate it

[@exol4229]

Thankyou!

[@s.p6482]

💖 from West Bengal

[@saisameer5842]

👌👌👌❤

[@zahidrasoolkhan2277]

Love from kashmir

[@lakshakumarlariya6821]

❤❤❤❤❤❤

[@jeffjo8732]

1) The interval [0,1] is indeed uncountable. (Note that you did not exclude 0.0000... or 0.11111... from the set you used, so the set is [0,1], not (0,1).) 2) Cantor's Diagonal Argument proves it. 3) This video is not a correct demonstration of CDA, and does not prove it. It is close, but incomplete. In fact, most expositions of CDA fail this way. It fails because you can't just say "we assume this list is complete" and then, when you show it is missing a number, claim a proof by contradiction. You have to actually use the assumed fact in the proof that leads to the missing number. All you really assumed is a list of some real numbers in that interval. What is shown in the video, is that if you have a list of any subset of [0,1], then that subset does not include the number B. This is the first part of CDA (actually, it is about strings, not numbers, but it does work with numbers). Only once this *_lemma_* is proven, directly and not by contradiction, does Cantor assume that the full set can be listed. Then we get the contradiction that B is in the listed set (since it includes all) but also not in the set (by the lemma). In other words, the contradiction is about B, not the interval.

[@RahulMapariBasicMaths]

Thank you so much for this information.

[@aakritibhuriya1484]

thank you sir !

[@sushmithabts229]

Thank you so much sir

[@barasharanidas7265]

Thank you sir....