Learning Points from Dennis Wildfogel’s TEDEd Talk on “How Big is Infinity?”

A geeky one here on set theory and infinity. When Buzz Lightyear says “to infinity and beyond!” in Toy Story, I guess he really knows what infinity means, such that there can be a “beyond” beyond infinity.

https://ed.ted.com/lessons/how-big-is-infinity#review

So there are infinitely many whole numbers, and infinitely many fractions. These 2 sets have the same scale of infinity, whereby you can match each element in each set to a corresponding one in the other set. However, the infinity of irrationals is bigger than the infinity of fractions. Then there’s the continuum hypothesis, which suggests that there are infinities of size between that of numbers and decimals. Interestingly enough, mathematicians managed to prove that the hypothesis cannot be proven false, nor can it be proven to be true. It’s one of those weird unanswerable questions in mathematics. I guess scientists shouldn’t feel so bad if they cannot come up with a unified theory of everything since even mathematics itself has such limitations.

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