Some infinities are BIGGER than other infinities! — Transcript

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1. 0:00I don't know if how many people know
2. 0:00this, but often it's mind-blowing when
3. 0:03you learn
4. 0:04that some infinities [music] are bigger
5. 0:05than others.
6. 0:07>> [laughter]
7. 0:08>> Joe Rogan just leaned 2 ft away from the
8. 0:10microphone.
9. 0:12Yeah, not all infinities are the same
10. 0:15size.
11. 0:15>> But if it's infinity, then it's
12. 0:17infinity. It's infinite. What is no?
13. 0:19>> Well, okay. Don't you remember when you
14. 0:21were a kid? They said, "What's the
15. 0:22biggest number you know?" "A million."
16. 0:23"Well, there's a million and one." Okay,
17. 0:24how about a billion? "Well, there's a
18. 0:25billion and one." There's the annoying
19. 0:26kid who always added one to it.
20. 0:28[clears throat] Okay, how about
21. 0:28infinity? "Well, infinity and one."
22. 0:30Okay, well, turns out infinity and one
23. 0:31and infinity are the same [music]
24. 0:33numbers. So,
25. 0:34so for example, the number of of
26. 0:37counting numbers, [music] so 1 2 3 up to
27. 0:40infinity, okay?
28. 0:41>> Right.
29. 0:41>> The numbers you would use to count
30. 0:43things, [music]
31. 0:43that's infinite. The number of
32. 0:46irrational numbers, so the numbers that
33. 0:48you cannot represent as a fraction,
34. 0:50okay?
35. 0:51That there's [music] more
36. 0:54There're more of those than there are
37. 0:55counting numbers, by far. So, these are
38. 0:57orders of infinity.
39. 0:58>> What what confuses me is the word
40. 1:00infinity cuz I had [music] always taken
41. 1:01the word infinity to mean something that
42. 1:02has no end. So, how can something that
43. 1:04has no end be larger than something else
44. 1:06that has
45. 1:06>> So, the way they do that mathematically,
46. 1:08the way to demonstrate [music] that
47. 1:09mathematically is you you map one item
48. 1:12in the set of this infinity to
49. 1:15corresponding items [music] in the set
50. 1:16of the other other infinity. And so, you
51. 1:18do this. So, you take the one and you
52. 1:20map it to like the first [music]
53. 1:21transcendental number. Take the two to
54. 1:23the second. You just keep doing this.
55. 1:25And when you do that mathematically,
56. 1:27what you find that one infinity
57. 1:29outstrips the other infinity.
58. 1:31>> Wow.
59. 1:31>> And then you're left with more
60. 1:33>> [music]
61. 1:33>> with more numbers. So, that shows you
62. 1:34that you have a bigger infinity.