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!