Cardinality of Sets | Countable Sets | Uncountable Sets | Set Theory | Maths for CS | CS Connect 29

Описание: This video will explain about cardinality of sets with respect to countable sets and uncountable sets. Practice problems are provided to aid the understanding of the concepts.

00:00 Intro
00:15 Cardinality of Sets
02:37 Countable Sets
04:17 Examples of countable set
06:22 Examples of uncountable set
08:57 -Cantor diagonalization argument
09:11 Union operation in countable sets
10:15 Schroder-Bernstein Theorem
15:21 Uncomputable Functions
16:17 The Continuum Hypothesis
20:12 Practice Problems
20:15 1. Determine whether each of these sets is countable or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set.
24:13 2. Give an example of two uncountable sets A and B such that A intersection B is finite, countably infinite and uncountable.
27:53 3. Show that Z x Z is countable by showing that the polynomial function f(m,n) = (m+n-2)(m+n-1)/2 + mis one-to-one and onto.

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