thattommyhall
April 12, 2013
180

# Grasping Infinity

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

April 12, 2013

## Transcript

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

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

3. Tours

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

5. 1 -> 10
2 -> 100
3 -> 1000
...

6. Cardinality

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

8. Countable?

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

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

11. Is Countable?

12. Is (0,1) countable?

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

14. 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.....

15. Is 'larger'?

16. Is 'larger'?

17. Is 'larger'?
0.8236...
0.2146...

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

19. Convergence

20. Building everything from nothing

21. S(n) = P(n)

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

23. To , and beyond!

24. Climbing Mount

25. 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?

26. 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,.

27. 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/