https://numath.com/wiki/ 2026-05-05T20:57:32+0000 https://numath.com/wiki/ https://numath.com/wiki/lib/tpl/numathtemplate/images/favicon.ico text/html 2019-09-03T22:32:08+0000 Anonymous (anonymous@undisclosed.example.com) https://numath.com/wiki/doku.php?id=topics:start&rev=1567549928&do=diff Mathematical topic articles This page is meant for articles about a mathematical topic of general interest. * Example article ---------- Create a new topic page: text/html 2019-08-09T16:52:15+0000 Anonymous (anonymous@undisclosed.example.com) https://numath.com/wiki/doku.php?id=topics:the_fundamental_theorem_of_algebra&rev=1565369535&do=diff The fundamental theorem of algebra Theorem: Any non-constant polynomial over $\mathbb{C}$ has a zero. Proof: Let $f(z)$ be a polynomial. Assume by contradiction that $f(z)$ does not have a zero. Define a function $g(z) = \frac{1}{f(z)}$. Then $g(z)$ is an entire function, and satisfies $\lim_{z\to\infty} g(z) = 0$. Since it is also bounded in any compact set, it follows that $g(z)$$g(z)$$f(z)$