S01.8 Countable and Uncountable Sets

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MIT RES.6-012 Introduction to Probability, Spring 2018
Instructor: John Tsitsiklis

License: Creative Commons BY-NC-SA

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Thanks, I‘ve been rereading my lecture notes for a week now, and only thanks to your videos I understand what countable and uncountable means!

daviddegenhardt

This is so clear and helpful. It heals my brain after having the maths class at

xiaozaowang

k = (m + n - 1)(m + n - 2)/2 + m
obtaining the sequence

1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ....
Nevertheless there will always remain as many not enumerated fractions as at the start.

undercherries

Thanks a lot for this amazing lecture ☺

SecretEscapist

We check the number of indexes by bijecting them with the fractions of the first column (we could use every other column or line as well). When applying the indexes for indexing fractions such that m/n gets the index
k = (m + n - 1)(m + n - 2)/2 + m
with the result
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
then the integer fractions have to supply these indexes. They are stripped off these indexes. The numnber of not indexed fractions remains constant.

Can you accept this argument or can't you?

undercherries

I slept in university, but studied in the university of youtube!

YuyangZhang-rr

could you really exhaust natural, rational, etc numbers ? how ? dont they just go to infinity ?

also why does a set in an interval makes it uncountable ?

if we talk about (0, 1) in natural number, then the set will be just empty.

maybe i'm missing something that everybody here knows already, but it is very counter-intuitive for me.

RFsalman

Just me that went here to learn this for powerscaling?

tsunayoshitsuna

How does tracing that path in the i-j axis represent the pairs of positive integers?

Ava-wtdb

ΕΙΣΑΙ ΕΛΛΗΝΑΣ ΜΟΝΟ ΚΑΙ ΑΠ ΤΗΝ ΠΡΟΦΟΡΑ .

dimitrissoldatos

Sir why you say Omega but it's not a Omega its called unit of resistance, omega symbol is very different than this?

kedar_bhoomi

This vidoe did not really helped. Too less information.

rj-njuk

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