We have talked about infinity over the past couple of weeks, including
- We’ve seen videos about the Hilbert Hotel with infinitely many rooms: http://www.newscientist.com/blogs/nstv/2011/12/math-in-a-minute-welcome-to-hotel-infinity-paradox.html
- And we’ve seen a video about one of Zeno’s paradoxes, concerning a race between achilles and a tortoise: http://vimeo.com/1654232
- The Droste effect provides a visualization of infinity: http://www.webdesignerdepot.com/2009/09/50-stunning-examples-of-the-droste-effect/
- We learned about Georg Cantor, who developed a theory of infinity that allowed mathematicians to better understand infinity and also revealed that there are different sizes of infinity. However, most mathematicians hated the theory and felt that Cantor was destroying mathematics. Here’s some video about this: http://www.dailymotion.com/video/xdoe8u_dangerous-knowledge-1-5_shortfilms (we watched most of the video in class, and will be watching some of the continuation of this video in the next class)
- Learned how to count. OK, you already knew this, but we talked about infinity and how the idea of one-to-one correspondence, which you learned when you were first counting (although you didn’t call it that) gives the key to infinity. See the notes from class here.