infinity_2010_upg

infinity_2010_upg, "The Capture of Infinity", a talk about Cantor's development of a consistent theory of infinity, given at the University of Pittsburgh at Greensburg, March 2010.

I have been working on a talk about Cantor's theory of infinity for some time now. I first planned to give this talk to the undergraduate math club at the University of Pittsburgh, Greensburg, during a visit in November 2009, but my schedule didn't work out. I kept working on the talk with a view to a February workshop at Virginia Tech, to be associated with the Center for Talented Youth, (run through Johns Hopkins University), which would have involved an audience of sixth graders and their parents (!). The idea of having to speak about serious mathematics to such an audience suggested more strongly that I should keep working on the topic of infinity, an engaging subject whose paradoxes can be understood without a great deal of prerequisites. Of course, the CTY workshop has been cancelled, but I continue to work at the notes, thinking I may end up giving this talk at UPG after all, perhaps in March 2010.

• infinity_2010_upg.tex
• infinity_2010_upg.pdf

The following files constitute the LaTeX file:

• achilles.png, an image of Achilles running, illustrating one of Zeno's paradoxes.
• cantor.png, an image of Georg Gantor, who developed set theory, and then consistent and convincing theories of infinite cardinal numbers (which measure size) and infinite ordinal numbers (which record order).
• euclid.png, whose proof of that there is no largest prime established a pattern of argument repeated through mathematical history, and which also showed that infinite objects existed, even if we refused to actually consider them directly.
• fourier_equation.png, an image of a very simple oscillatory function, suggesting the many zeroes such a function can have.
• galileo.png, an image of Galileo Galilei, one of the first to consider a paradox of infinity and have something insightful to say about it.
• infinity_2010.tex, the LaTeX source;
• nail.png, an image of a nail, suggesting a finite 1D line segment that can be "rearranged" to form the Titanic.
• quadratic_equations.png, an image of some quadratic equations with just a few zeroes.
• rationals.png, an image of a table that suggests how all the (positive) fractions can be counted.
• sheep.png, an image that suggests counting sheep.
• stairway_to_heaven.png, an image of a "stairway to heaven", suggesting the endless series of infinities that Cantor uncovered.
• titanic.png, an image of the Titanic, a big 3D object that has no more points than a 1 inch line segment.
• vt_invent_logo.pdf, a logo.
• wooden_blocks.png, an image of wooden blocks forming a cube, suggesting how Albert of Saxony's infinite beam could be rearranged to fill space.
• zeno.png, an image of Zeno, poser of several paradoxes.