Integers & Rationals are both infinite but is it the SAME infinity?

What does it mean for two infinite sets to have the same size? For instance, are the Integers and the Rationals (numbers like 2/3) the same size? They are certainly both infinite, but the question is whether infinite really only represents one concept or whether it divides into multiple concepts.

In this video we investigate a notion called "countable" which extends from the basic way we count finite sets. According to that notion, the integers and the rationals have the same size.

In the next video we will compare the integers and the REAL numbers.

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Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!

Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.

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