Android, LaTeX, Termial and Surreal Numbers

Donald Ervin Knuth
January 10, 1938 (age 79)
Milwaukee, Wisconsin, U.S.

It was with great surprise that I discovered my LaTeX-based equations in the two previous posts were not displaying using the Chrome browser on my Android phone. I checked using the default Internet browser and the result was the same. I checked on my iPad, using both Chrome and Safari, and all was well. On Ubuntu (under VirtualBox), using Firefox, and in Windows (under VirtualBox), using Microsoft Edge and Chrome, there was again no problem.

It was only Android, at least version 5 which I'm using on my Note 3. Maybe there is support for LaTeX in the 6 and 7 versions of Android. However, there's surprisingly little information about this problem and certainly no open admission anywhere that LaTeX isn't supported by Android.

This leads on to the term termial. I stumbled across it as I researched LaTeX because its creator, Donald Knuth, invented the term in his The Art of Computer Programming. It was devised as an analogy of the factorial, so as to illustrate the extension of the latter to the real numbers. It's defined as follows:

Let n \(\in\) ℤ > 0 (that is a positive integer) then n? = \(\sum_{k=1}^{n} k \)

Let n \(\in\) ℝ (that is a real number) then n? = \(\frac{n(n+1)}{2}\)

So 4? = 4 + 3 + 2 + 1 = 10 and \(\frac{1}{2}\)? = \(\frac{3}{8}\)

The second formula works for integers because 4? = 4 x 5 ÷ 2 = 10.

Donald Knuth is certainly an interesting character. This is a link to his biography on Wikipedia. He wrote a book called Surreal Numbers and below is a video in which he discusses the inspiration behind the idea of surreal numbers and how he actually set about writing the book in six days.

The book is freely available on the Internet and I've downloaded a copy and added it to my library.