Cardinality vs. Dimension of Sets

This is a short video, designed to be watched between classes 4 and 5 of Math 339: Linear Algebra. It covers the definitions of cardinality and finite/countable/uncountable sets, and introduces the idea of dimension of a vector space. [Class 5-1]

Table of Contents:

00:00 - Introduction
00:24 - Cardinality Introduction
02:11 - Definition of Equinumerous
03:49 - Example of Bijective Counting
05:44 - Definitions of Finite, Countable and Uncountable Sets
08:21 - Definition of Cardinals
11:53 - Crazy Bijections
12:45 - Definition of Dimension
15:00 - Next Time

[MindGameArcade]

I don't get it, the explanation at the end about dimensions is too quick. To me it still seems that we can represent dimension 2 in R so why do they have a different dimension. Any couple of vector can be represented in R so why do we need R²

[atiurrahman]

Very good explanation mam. Please explain for me at least the topology in an easy way.