Monthly Archives: March 2006

My favorite number

I finally have a favorite number. Well, actually, I have one favorite number for every well-ordering of the real numbers. If you don’t believe in the axiom of choice, I don’t have any favorite numbers.

Let (< ) be a well-ordering of the real numbers. There are aleph-0 many sequences of characters, and 2^aleph-0 (which is strictly larger than aleph-0) many real numbers. Therefore, there must be a real number which is not describable in words. My favorite number is the least such number according to the well-ordering.

Uh oh… I think I just described it in words.

Forced Free Software

I saw something rather depressing when I went to the sourceforge home page today. The five most downloaded projects were: eMule, Ares Galaxy, Azureus, Shareaza, and The GIMP for Windows, in that order. Notice anything about those. Four of those five are file sharing clients. So people are using open source software not as a substitute for commercial software, but instead as a means to use commercial software for free. Hmph. I guess it’s nice to see that a solid open source substitute for Photoshop is actually getting used, though.