Year: 2015

What is the horizontal line test?

High School Algebra, High School Mathematics

In January of this year, we have discussed about the vertical line test. We have learned that if a vertical line intersect a graph more than once, then that graph is not a function. In this post, we learn about the horizontal line test and its relation to inverse functions.

Suppose we have a function f. Then, we input x and call the output f(x). If we do things backward, suppose we have the number y which is in the range of f. What value should we input to f to get y? Let’s have a more specific example.

Suppose we have the function f(x) = x^2. And we choose the number y = 9 which is in the range of f. What number should we input in f to get 9? Well, we will have two numbers, those are 3 and -3. » Read more

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Banach-Tarski Paradox and A Great Discussion About Infinity

College Mathematics

This video is a rich discussion about about infinity. It starts from the famous infinite chocolate problem, countable infinity, uncountable infinity, Cantor’s diagonalization system, Hilbert’s hotel, and the Banach-Tarski Paradox. Although the last part is a bit too much for the level of this blog, the explanations before it of the concepts before it are extremely clear and helpful.

I had several discussions about infinity in this blog particularly the content of Counting the Real Numbers, The Grand Hotel Paradox, and One to One Correspondence. You might want to check them out.

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