In this post, I show that $\lim_{x\rightarrow a}[f(x) – g(x)] = \lim_{x \rightarrow a} f(x) – \lim_{x \rightarrow a} g(x)$ given that $\lim_{x \rightarrow a} f(x) = A$ and $\lim_{x \rightarrow a}… Read more Limit of a Sum of Two Functions In this post, I show that$ \lim_{x \rightarrow a} [f(x) + g(x)]$is equal to$\lim_{x \rightarrow a}f(x) + \lim_{x \rightarrow a} g(x)$given that$ \lim_{x \rightarrow a}f(x) = A$and$ \lim_{x \rightarrow a}g(x)…

The triangle inequality for real numbers is $|a+b| \le |a| + |b|$ in which $a$ is a variable for a real number, and $b$ is a variable for a real number. Proof:…
In this post, I prove that $|xy| = |x||y|$ in which $x$ is a variable for any real number and $y$ is a variable for any real number. This is done by…