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How big is infinity

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Information about How big is infinity
Technology

Published on March 7, 2014

Author: Shaunakde1

Source: slideshare.net

Description

A 10 min introduction to the work of cantor
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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. 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…

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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