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# How big is infinity

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A 10 min introduction to the work of cantor

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### How big is infinity

1. 1. HOW BIG IS INFINITY? Shaunak De
2. 2. ODDLY AND EVENLY PERPLEXING There are as many even number as there are odd numbers
3. 3. MAKE A LIST OF ALL THE FRACTIONS?
4. 4. MAKE A LIST OF ALL THE FRACTIONS?
5. 5. MAKE A LIST OF ALL THE FRACTIONS?
6. 6. Some numbers are insane!
7. 7. “STOP BEING IRRATIONAL!” ~ CANTOR’S WIFE Ratios of “Whole Numbers” RATIONALS Others NON - RATIONALS
8. 8. “STOP BEING IRRATIONAL!” ~ CANTOR’S WIFE Ratios of “Whole Numbers” RATIONALS Others IRRATIONALS
9. 9. SO CAN WE MAKE A LIST OF ALL THE DECIMALS?
10. 10. SO CAN WE MAKE A LIST OF ALL THE DECIMALS? No!
11. 11. SO CAN WE MAKE A LIST OF ALL THE DECIMALS? Not merely that we don’t know how, but that it can’t be done.
12. 12. YOU’RE WRONG. ET DID IT. Sr. No. 1 2 3 4 … Number 2.13698548756963221485 1.73653236695875236333 6.369369521896327895 7.125169362145696365 …
13. 13. “I’M GONNA WATCH YOU FAIL” ~ CANTOR Sr. No. 1 2 3 4 … Number 2.13698548756963221485 1.73653236695875236333 6.369369521896327895 7.125169362145696365 … N = 0.2112…
14. 14. 1 0
15. 15. 0
16. 16. HOW BIG IS YOUR INFINITY? Set of all subsets of an infinite set, yields a larger infinite set
17. 17. THERE ARE AN INFINITE NUMBER OF INFINITIES OF DIFFERENT SIZES!
18. 18. THE CONTINUUM HYPOTHESIS
19. 19. FULLY BOOKED!