-\begin{itemize}
- \item The document is expressed in DOM format using XML/HTML/SVG
- \item A Javascript program is run which can modify the DOM
- \item At a high level this may be simply changing attributes of elements dynamically
- \item For low level control there is canvas2D and even WebGL which gives direct access to OpenGL functions
- \item Javascript can be used to make a HTML/SVG interactive
- \begin{itemize}
- \item Overlooking the fact that the SVG standard already allows for interactive elements...
- \end{itemize}
- \item Javascript is now becoming used even in desktop environments and programs (Windows 8, GNOME 3, Cinnamon, Game Maker Studio) ({\bf shudder})
- \item There are also a range of papers about including Javascript in PDF ``Pixels or Perish'' being the only one we have actually read\cite{hayes2012pixels}
- \begin{itemize}
- \item I have no idea how this works; PDF is based on PostScript... it seems very circular to be using a programming language to modify a document that is modelled on being a (non turing complete) program
- \item This is yet more proof that people will converge towards solutions that ``work'' rather than those that are optimal or elegant
- \item I guess it's too much effort to make HTML look like PDF (or vice versa) so we could phase one out
- \end{itemize}
-\end{itemize}
+Consider a value of $7.25 = 2^2 + 2^1 + 2^0 + 2^{-2}$. In binary (base 2), this could be written as $111.01_2$ Such a value would require 5 binary digits (bits) of memory to represent exactly in computer hardware. Some values, for example $7.3$ can not be represented exactly in one base (decimal) but not another; in binary the sequence $111.010\text{...}_2$ will never terminate. A rational value such as $\frac{7}{3}$ could not be represented exactly in any base, but could be represented by the combination of a numerator $7 = 111_2$ and denominator $3 = 11_2$. Lastly, some values such as $e \approx 2.81\text{...}$ can only be expressed exactly using a symbolical system --- in this case as the result of an infinite summation --- $e = \displaystyle\sum_n=0^{\infty} (-1)^{n}\frac{1}{n!}$