HOW BIG IS INFINITY? Shaunak De
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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. Number
1 2.13698548756963221485
2 1.73653236695875236333
3 6.369369521896327895
4 7.125169362145696365
… …
“I’M GONNA WATCH YOU FAIL” ~ CANTOR
Sr. No. Number
1 2.13698548756963221485
2 1.73653236695875236333
3 6.369369521896327895
4 7.125169362145696365
… …
N = 0.2112…
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!
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