Real euclidean spaces Real euclidean spaces have definitions of inner product and norm. Examples in \(\mathbb R^n\):
The usual inner product The unit-radius circumference when considering an unusual inner product Cauchy-Schwarz inequality Let \(V\) be a real vector space. A form or real function \[ \begin{aligned} \langle\cdot,\cdot\rangle\colon V\times V &\rightarrow \mathbb R \\ (x, y) &\mapsto \langle x,y\rangle \end{aligned}\ \] is said to be an inner product if, for all \(x, y, z \in V\) and all \(\alpha \in \mathbb R\),

In the Digital Era, copyright has become harder to enforce than ever before. Digital works are subject to copying without any quality degradation, which encourages piracy and can lead to market failure [1, p.118]. While some optimists [2, p.236] claim that digital rights management (DRM) is a successful technology, protecting copyrights in the digital world, and safeguarding markets and creators alike, the truth is quite the opposite. Since current implementations of DRM unjustly and broadly harden access to copyrighted works, they represent a disconnect with the fundamental concepts of copyright, breaking with the Lockean principles for appropriation which are the bedrock for property rights.

I have always been a proud and happy iPhone user. My first smartphone was an iPhone 3G and, although I had owned a couple Motorola flip-phones before that, I consider it to be the first phone I really used. I had no complaints; from when I first got it circa 2008 to when I decommissioned it in favor of the iPhone 5, some 4 years later, it worked fairly well.

Let a statement be any sentence of form
\[ \mathcal S + \phi \]
Where \(\mathcal S\) is a subject and \(\phi\) is a predicate. The sentences “Spinoza died in the Hague”, and “Grey is grey”, for example, qualify as statements. In the first, we have “Spinoza” as the subject, and “died in the Hague” as the predicate. Note that, for a sentence to qualify as a statement, its predicate does not need to contain an object (consider the sentence \(X\text{ is.

This is a follow up to my previous post on how to run Debian on the Nspire, this time we will be going deeper into the matter and compiling the Linux Kernel ourselves, and doing such in a way that it’s compatible with Arch Linux ARM
Hardware requirements The requirements for this project are the same as for the last one, here’s what you’ll need:
A Texas TI Nspire CX or CX CAS USB Hub Mini-B OTG USB Cable USB Drive Setting everything up Since we will be building the Kernel ourselves this time we will need to do some special work on our setup, in particular to our build environment.