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Grasping Infinity

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

thattommyhall

April 12, 2013
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  1. @thattommyhall
    Theatre fan, occasional mountaineer, part time
    runner, thoroughly nice chap, available in fine
    bookstores everywhere
    http://www.thattommyhall.com

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  3. (img from http://world.mathigon.org/Infinity.html)

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  8. Tours

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  9. 1 -> 1
    2 -> 4
    3 -> 9
    ...

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  10. 1 -> 10
    2 -> 100
    3 -> 1000
    ...

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  11. Cardinality

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  13. Countable?
    ..., -3, -2, -1, 0, 1, 2, 3 ...

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  14. Countable?

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  18. Powersets
    P(S) = The set of all subsets of S

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  19. S = {a,b,c}
    P(S) = { {}, {a}, {b}, {c},
    {a,b},{b,c},{a,c},
    {a,b,c} }

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  20. Is Countable?

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  21. Is (0,1) countable?

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  22. Is (0,1) countable?
    1 -> 0.165198165161681681681681681...
    2 -> 0.1565516516816543576432135...
    3 -> 0.516516846516598498468498468...
    4 -> 0.516168489465435473543214354354...
    5 -> 0.1
    6 -> 0.454648976874354672546849846...

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  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.....

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  24. Is 'larger'?

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  26. Is 'larger'?

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  27. Is 'larger'?
    0.8236...
    0.2146...

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  28. Is 'larger'?
    0.8236...
    0.2146...
    0.82213466...

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  33. Convergence

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  35. Building everything from nothing

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  37. S(n) = P(n)

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  40. Ordinality
    one, two, three
    VS
    first, second, third

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  41. To , and beyond!

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  45. Climbing Mount

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  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?

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  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,.

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  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

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