Grasping Infinity

Slide #37 is a mistake! I think it caused me to mispeak and led to confusion!

From Bacon 2013
http://devslovebacon.com/conferences/bacon-2013/talks/grasping-infinity

Transcript

1. @thattommyhall Theatre fan, occasional mountaineer, part time runner, thoroughly nice chap, available in fine bookstores everywhere http://www.thattommyhall.com
3. (img from http://world.mathigon.org/Infinity.html)
8. Tours
9. 1 -> 1 2 -> 4 3 -> 9 ...
10. 1 -> 10 2 -> 100 3 -> 1000 ...
11. Cardinality
13. Countable? ..., -3, -2, -1, 0, 1, 2, 3 ...
14. Countable?
18. Powersets P(S) = The set of all subsets of S
19. S = {a,b,c} P(S) = { {}, {a}, {b}, {c}, {a,b},{b,c},{a,c}, {a,b,c} }
20. Is Countable?
21. Is (0,1) countable?
22. Is (0,1) countable? 1 -> 0.165198165161681681681681681... 2 -> 0.1565516516816543576432135... 3 -> 0.516516846516598498468498468... 4 -> 0.516168489465435473543214354354... 5 -> 0.1 6 -> 0.454648976874354672546849846...
23. Is (0,1) countable? 1 -> 0.165198165161681681681681681... 1 -> 0.1565516516816543576432135... 1 -> 0.516516846516598498468498468... 1 -> 0.516168489465435473543214354354... 1 -> 0.1 1 -> 0.454648976874354672546849846... r = 0.267219.....
24. Is 'larger'?
26. Is 'larger'?
27. Is 'larger'? 0.8236... 0.2146...
28. Is 'larger'? 0.8236... 0.2146... 0.82213466...
33. Convergence
35. Building everything from nothing
37. S(n) = P(n)
40. Ordinality one, two, three VS first, second, third
41. To , and beyond!
45. Climbing Mount
52. Monkey Puzzle Monkey 1: Opens all the doors Monkey 2: Starts at 2, goes up in 2s and 'toggles' each door. ... Monkey N, Starts at N, goes up in Ns and 'toggles' each door ... What doors are left open?
59. Everything would be in its blind volumes. Everything: the minutely detailed history of the future, the archangels' autobiographies, Aeschylus' The Egyptians, the exact number of times that the waters of the Ganges have reflected the flight of a falcon, the secret and true nature of Rome, my dreams and half-dreams at dawn on August 14, 1934, the proof of Fermat's last theorem, the paradoxes Berkeley invented concerning Time but didn't publish, the premature epiphanies of Stephen Dedalus, which would be meaningless before a cycle of a thousand years, the Gnostic Gospel of Basilides,the commentary on that gospel, the commentary on the commentary on that gospel, the true story of your death, the translation of every book in all languages, the interpolations of every book in all books, the song the sirens sang, the complete catalog of the Library, thousands and thousands of false catalogues, the demonstration of the falsity of those catalogues, the demonstration of the falsity of the true catalogue, Everything. but for every sensible line or accurate fact there would be millions of meaningless cacophonies, verbal farragoes, and babblings. Everything: but all the generations of mankind could pass before the dizzying shelves ever reward them with a tolerable page,.
60. Refs • http://world.mathigon.org/Infinity.html • http://naturelovesmath-en.blogspot.co.uk/2012/07/infinity-and-transfinite- numbers.html • http://scientopia.org/blogs/goodmath/category/surreal-numbers/ • http://maskofreason.files.wordpress.com/2011/02/the-library-of-babel-by- jorge-luis-borges.pdf •