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How big is infinity
The document discusses the concept of infinity and different types of infinite numbers and sets. It notes that there are an infinite number of rational numbers but also an infinite number of irrational numbers. It also discusses Georg Cantor's work showing that some infinite sets are larger than others, such as the set of all subsets of an infinite set being larger than the original infinite set. The document concludes by mentioning Cantor's continuum hypothesis regarding the possible sizes of infinite sets.
How big is infinity
- 1. HOW BIG ISINFINITY? Shaunak De
- 2. ODDLY AND EVENLY PERPLEXING Thereare as many even number as there are odd numbers
- 3. MAKE A LISTOF ALL THE FRACTIONS?
- 4. MAKE A LISTOF ALL THE FRACTIONS?
- 5. MAKE A LISTOF ALL THE FRACTIONS?
- 6. Some numbers areinsane!
- 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 WEMAKE A LIST OF ALL THE DECIMALS?
- 10. SO CAN WEMAKE A LIST OF ALL THE DECIMALS? No!
- 11. SO CAN WEMAKE 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. ETDID IT. Sr. No. 1 2 3 4 … Number 2.13698548756963221485 1.73653236695875236333 6.369369521896327895 7.125169362145696365 …
- 13. “I’M GONNA WATCHYOU FAIL” ~ CANTOR Sr. No. 1 2 3 4 … Number 2.13698548756963221485 1.73653236695875236333 6.369369521896327895 7.125169362145696365 … N = 0.2112…
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- 16. HOW BIG ISYOUR INFINITY? Set of all subsets of an infinite set, yields a larger infinite set
- 17. THERE ARE AN INFINITENUMBER OF INFINITIES OF DIFFERENT SIZES!
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