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Shaunak De
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A 10 min introduction to the work of cantor
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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!
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