Maynard's math and stuff

The website index.

My github is @Quelklef

The definition of associativity of an operator $\cdot$ is that $a \cdot (b \cdot c) = (a \cdot b) \cdot c$. Let view $a$ and $b$ as actions, and $c$ as an object. This can be more easily done by making the variable replacements $f = a$, $g = b$, $x = c$ to produce $f \cdot (g \cdot x) = (f \cdot g) \cdot x$. Now associativity reads as a statement about composition, and indeed looks very close to the definition of composition, $f(g(x)) = (f \circ g)(x)$.

A compression algorithm can be thought of simply as a function $: F \to F$ over the set of files $F$. Under this interpretation, lossless algorihms are bijective functions. Though a lossless algorithm cannot compress every file, we usually don't actually care about compressing every file; because of this, there are clever ways to reach desired behaviour.

Parentheses are used a lot: for functions, e.g. $f(x)$, tuples, e.g. $(0, 2)$, ideals, e.g. $\mathbb Z / (4)$, and a bunch more. This is a collection of these different uses.

Vector-based proof that a line splits a plane into two parts.

A Lower Bound and Approximation for the Van der Waerden Number Function $W(c, k)$

Ruminations on shoes.

My email is eli.t.maynard@gmail.com

My twitter is @Quelklef.

A mailing list sign up.

A strange problem I had when coding.

Keyboard-only minesweeper

Proving that $f(a + b) = f(a) + f(b) \implies f(cx) = cf(x)$ is pretty easy when $c$ is an integer or a rational. But does it generalize to real $c$? As it turns out, no, but it comes close. This is a mistaken proof of generalization to real $c$ with a discussion of the subtle error made.

Interactive propositional and first-order logic proof helper

Interactively visualize the $\varepsilon$-neighborhoods of complex-analytic functions.