The Number of Points on Two Line Segments

We say that a set is countably infinite if we can pair the elements with set of counting numbers 1, 2, 3, and so on. Believe it or not, the number of positive integers and the number of integers (both negative and positive including 0) have the same number of elements. It is because we […]
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Are all infinities created equal?

A one-minute explanation that not all infinities are equal. The video shows that the number of real numbers from 0 to 1 is  greater than the number of all natural numbers 1, 2, 3, 4, and so on. If the video is too fast or too short, you can read a more detailed explanation in […]
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Is 0 a natural number?

When I was still teaching,  several of my students asked me this: Is 0 a natural number? Short Answer It depends on the convention. In some references, the set of natural numbers includes 0. In other references, the set of natural numbers does not include 0. Long Answer When we define a particular mathematical concept, […]
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