HOW BIG IS INFINITY?

Shaunak De
ODDLY AND EVENLY
PERPLEXING

There are as many even number
as there are odd numbers
MAKE A LIST OF ALL THE
FRACTIONS?
MAKE A LIST OF ALL THE
FRACTIONS?
MAKE A LIST OF ALL THE
FRACTIONS?
Some numbers are insane!
“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
7.12...
“I’M GONNA WATCH YOU FAIL”
~ CANTOR
Sr. No.
1
2
3
4
…

Number
2.13698548756963221485
1.73653236695875236333
6.369369521896...
1

0
0
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!
THE CONTINUUM
HYPOTHESIS
FULLY BOOKED!
How big is infinity
How big is infinity
How big is infinity
How big is infinity
How big is infinity
How big is infinity
How big is infinity
How big is infinity
Upcoming SlideShare
Loading in …5
×

How big is infinity

520 views

Published on

A 10 min introduction to the work of cantor

Published in: Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
520
On SlideShare
0
From Embeds
0
Number of Embeds
15
Actions
Shares
0
Downloads
11
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

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!

×