Mathematics

Resistance to complex math seems to never die out.  I see it frequently in PF posts.  Often it takes the form of challenges rather than questions. …

At the first sight, there are many paradoxes in complex number theory. Here are some nice examples of things that don't seem to work:Example A [itex]-1=i^2=\sqrt{-1}\cdot\sqrt{-1}=\sqrt{(-1)(-1)}=\sqrt{1}=1[/itex]Example…

Partial fractions decomposition is an algebraic technique that can be used to decompose (break down) a product of rational expressions into a sum…

In this Insights article we'll look at a limited class of ordinary differential equations -- homogeneous linear ODES with constant coefficients. Although…

Why do people say 1 and 0.999... are equal? Aren't they two different numbers? No — 1 and 0.999... really are the same number, although that can feel…

  The previous article ended with the concept of classical locally variational field theories, of which a class of examples are…

Introduction This FAQ is about proofs. Proofs are central to mathematics, and writing proofs is a skill many people find hard to master. There are two…

Yes. What 0.999... Means First, we have not addressed what 0.999... means. So it is best to first describe what the notation [tex]b_0.b_1b_2b_3...[/tex]…

1. Classifying as discrete, continuous, or mixed These statements (or equivalents) can be found in authoritative-seeming websites:X "A random variable…

This is Part 2 of a series of articles in which the goal is to exhibit a continuous function that is nowhere differentiable and to explore some interesting…