Given a line $y = \alpha x$ and a point $(a, b)$ in $\mathbb{R}^2$, I derived the distance formulas for the $L^1$, $L^2$, and $L^\infty$ norms in closed form as follows: $L^1$ distance: $\space \space d_{L^1} = |a \alpha - b|\cdot \min(1,\frac{1}{|\alpha|})$ $L^2$ distance: $\space \space d_{L...

This is a question from Dummit & Foote. Let G be a group of order 203. Prove that if H $\leq$ G is a normal subgroup of order 7 then H $\leq$ Z(G). Hence prove that that G is abelian. My attempt: H is a subgroup of prime order, so it is cyclic and hence abelian. This means $H \leq C_G(H)$...

One of my biggest pet peeves with traditional mathematical pedagogy is the ubiquity of non-semantic names (naming things after people being the typical offense...), even when an appropriate semantic identifier of similar length is available. For example, it costs basically nothing to say "freque...