Countable and Uncountable Sets (Part 2 of 2)

00:00 - How to show that a set is countable
00:36 - The set of integers is countable
01:19 - The set of rational numbers is countable
02:29 - The set of real numbers is uncountable
05:23 - Summary

[renewd]

You are a brilliant teacher. In the span of 15 minutes, I have shifted from a state of mind where I thought I might never be able grasp this concept (or want to), to a sense that it is very possible and coherent.

[hellahandsomee]

Easiest cardinality video to understand thanks man

[kaganhamzacebi]

I have listened more than 100 teachers who are trying to teach this topic and this lecture is the best by far. Thanks for fast and clean lecture you are the best!

[carlitozway]

ive been reading my textbook and watching videos for days, but only this video made it click. thank you.

[BestAccountNameEver]

this is by far one of the most clear explanation/tutorial i have seen on youtube! thank you!

[carolincloud]

This is extremely clear, I understand this more than my textbook! Thanks a ton! :)

[nyarbeinghi]

After 8 weeks I think I finally understand, and not only understand the difference between countable and uncountable, but how to prove them as well.

[paulineleung]

This is clear quality explanation. Thank you!

[elijahtapia]

Wonderful way to explain something my teacher failed to do in class. Many years later still helping the undergrad math majors!

[achillesarmstrong]

I watched this video 3 times this year. Such a good video

[dooham]

Thank you!!!! I thought no one would be able to teach discrete math in a clear concise way.

[nohopebutwhatwemake]

excellent explanation. My textbook is so dry and overblown it's barely readable. You actually make the lesson clear and concise. Thank you.

[jugglerfox]

Thank you so much! This explained it so well, I was stuck. MY MAN.

[gabrielgitonga]

Hello! I have learnt a lot today from your tutorial. Am grateful for the knowledge i have acquired
and may you be blessed more.

[achillesarmstrong]

wow. thumbs up. I watched 5 videos about this topic, you your explanation is the best! Good Job. Cheers

[hanachitsaz]

Thank you thank you thank you! So clear and easy to comprehend!

[crystal]

Wow, I can't say how thankful I am. My final is in a couple of days, and even though my professor just taught cardinality to us, it's expected to cover 25% of our exam. Now I can walk in more confident that I at least have a 25% lol...

[AffaanMansoori]

you just made my work very easy now i can complete my assignment !!!! THANK YOU

[SkyShattersWind]

Thanks a lot for this video. It helped me to get my head around countability and uncountability.

[MaxofWarcraft]

0 is an element of the set of Natural numbers. Therefore, to test for countability, you should look for a one-to-one correspondence with the set of positive integers, Z^{+}, which is {1, 2, 3, ...}, i.e. what Rob defines to be the set of Natural numbers. Note that you could also look for a one-to-one correspondence with the Natural numbers, that is including the 0; just be cautious as to how you define the set you're comparing with, as it might cost you points.