Proof Without Words: If x >0, x + 1/x >=2

A picture is worth a thousand words, even in mathematics. Sometimes, complicated algebraic expressions can be shown using very simple geometric representations. One example is the sum

$\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots$

which equals 1.

In this post, we show another proof without words. Proof without words is not a proof per se but rather a representation that will help readers understand a proof. » Read more

A Fascinating Introductory Video to Mathematical Proofs

I recently came a cross with a great introductory video about mathematical proofs titled How to Prove a Mathematical Theory. The video  which was produced by TED explains what is a mathematical proof, discusses a very brief history, and illustrates with an example. I hope you enjoy it as much as I did.

11 Proven Proof Techniques Non-Math Majors Should Know

Proofs is the heart of mathematics.  It is what differentiates mathematics from other sciences.  In mathematical proofs, we can show that a statement is true for all possible cases without showing all the cases. We can be certain that the sum of two even numbers is  even without adding all the possible pairs.

For those who are “non-math people,” the proof techniques below will help you, but the “math people” are probably those who are going to enjoy them more.  » Read more

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