How big is infinity

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Shaunak De

A 10 min introduction to the work of cantor

Technologie

ODDLY AND EVENLY
PERPLEXING

There are as many even number
as there are odd numbers

“STOP BEING IRRATIONAL!” ~
CANTOR’S WIFE
Ratios of “Whole
Numbers”

RATIONALS

Others

NON - RATIONALS

“STOP BEING IRRATIONAL!” ~
CANTOR’S WIFE
Ratios of “Whole
Numbers”

RATIONALS

Others

IRRATIONALS

SO CAN WE MAKE A LIST OF
ALL THE DECIMALS?

SO CAN WE MAKE A LIST OF
ALL THE DECIMALS?

No!

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.

YOU’RE WRONG. ET DID IT.
Sr. No.
1
2
3
4
…

Number
2.13698548756963221485
1.73653236695875236333
6.369369521896327895
7.125169362145696365
…

“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…

HOW BIG IS YOUR INFINITY?

Set of all subsets of an infinite set, yields a larger infinite set

THERE ARE AN
INFINITE NUMBER OF
INFINITIES OF
DIFFERENT SIZES!

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How big is infinity

1. HOW BIG IS INFINITY? Shaunak De

2. ODDLY AND EVENLY PERPLEXING There are as many even number as there are odd numbers

3. MAKE A LIST OF ALL THE FRACTIONS?

4. MAKE A LIST OF ALL THE FRACTIONS?

5. MAKE A LIST OF ALL THE FRACTIONS?

6. Some numbers are insane!

7. “STOP BEING IRRATIONAL!” ~ CANTOR’S WIFE Ratios of “Whole Numbers” RATIONALS Others NON - RATIONALS

8. “STOP BEING IRRATIONAL!” ~ CANTOR’S WIFE Ratios of “Whole Numbers” RATIONALS Others IRRATIONALS

9. SO CAN WE MAKE A LIST OF ALL THE DECIMALS?

10. SO CAN WE MAKE A LIST OF ALL THE DECIMALS? No!

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. YOU’RE WRONG. ET DID IT. Sr. No. 1 2 3 4 … Number 2.13698548756963221485 1.73653236695875236333 6.369369521896327895 7.125169362145696365 …

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. 1 0

15. 0

16. HOW BIG IS YOUR INFINITY? Set of all subsets of an infinite set, yields a larger infinite set

17. THERE ARE AN INFINITE NUMBER OF INFINITIES OF DIFFERENT SIZES!

18. THE CONTINUUM HYPOTHESIS

19.

20.

21. FULLY BOOKED!