Monday, January 1, 2017 Hipster Billy Budd I knew I had seen this before. Maybe it was at the gallery showing I was at last week with my brother. I was almost certain I had seen the work before and I was right. I knew it was the Paddington, that steampunk/punk looks like art mixed with industrial design meets steampunk that looks like high street fashion. I don’t know if the artist’s name is Paul Sotelo or not, but it appears he’s known as “Hipster Billy Budd.” Hipster Billy Budd is a reference to Herman Melville’s famous novella, Billy Budd and the Carpenter (1897), in which the titular character, Billy, is arrested for killing of his shipmate and fellow sailor, John Claggart (commonly known as “the Carpenter”), at the order of a senior officer. Billy is only saved when he convinces the senior officer of his innocence. After Billy’s acquittal, his life is tragically cut short. I never heard of a hipster being acquitted of a crime, but Hipster Billy Budd may be one of those punks who defy the system and are rewarded with a life of heroin and retro looks. I discovered Hipster Billy Budd by perusing Etsy over the Christmas holiday, especially the “Trash to Treasure” section. I’m always interested in anything with a steampunk-ish style. I’ve noticed that every artist or artist’s page on Etsy is devoted to steampunk style clothing. It’s hard to find actual steampunk clothing that’s ugly or as ugly as it has to be to be considered steampunk; all too often it’s a mixture of Pop, Industrial, and even retro. It’s almost difficult to find a perfectly steampunk look, but Hipster Billy Budd’s takes a steampunk look that goes the farthest out on the fringe but still keeps it consistent with steampunk at the same time. Although this is an Etsy page, it’s very easy to see that Hipster Billy Budd didn’t get the exposure he deserved. His shop is very small and his potential to make a lot of money by taking advantage of the Etsy stereotype of people who go against the system is limited. On the website, it also states

Q: If $a,b$ $\in$ $\mathbb{R}$, $a$ $\leq$ $b$ and $a$=$b$ $\Rightarrow$ $a$=$b$. Deduce from the following result that for any $\alpha, \beta$ $\in$ $\mathbb{R}$ such that $\alpha$ $\leq$ $\beta$, $\alpha$=$\beta$. Given that $\alpha$=$\beta$ $\Rightarrow$ $\alpha$+$\beta$= $\alpha$+$\alpha$=$\beta$+$\beta$=$\beta$, $\alpha$=$\beta$ $\Rightarrow$ $2\alpha$=$2\alpha$,$2\alpha$=$2\beta$, $2\alpha$=$2\beta$ $\Rightarrow$ $\alpha$+$\beta$= $\beta$. Is the result straightforward? I do not see the immediate reasoning. Would the quickest proof be induction? Thanks in advance for your support. A: Let $a\in\mathbb R$ be arbitrary. Then we have the following cases: $a\leq 0$ $a\geq 0$ $a=0$ Based on those cases, one can now conclude the desired statement: A: This is an application of how distributivity works. Suppose $x\in\mathbb{R}$. It will be convenient to call $2x$ a $2$ times $x$. It will also be convenient to say that if $x\in\mathbb{R}$, then $2x\in \mathbb{R}$ and vice versa. $2x=0\Rightarrow x=0$ $\alpha+2x\ge0\Rightarrow x\ge0$ $\alpha+2x\le0\Rightarrow x\le0$ $2x=0\Rightarrow x=0$ Influence of patient positioning, number of intraoral radiographs, and image modality on periapical size: an experimental study. The influence of various factors on periapical radiographs has been widely discussed. Among them, image modality has emerged as an important factor. This study aims to further