The cardinalities of the naturals and of the reals are more tightly coupled than you might think.
Post-release notes:
The diagonalization argument is incorrect due to a similar flaw as the one presented in the ending sequence. To fix it, construct the number as follows: take the nth digit of the nth number. If it's 7, make it a 0. If it's anything else, make it a 7. This takes care of the pesky case of the infinite strings of 9s that roll around to a 1 and infinitely many zeroes after it. Thanks @jbucata for the correction!
Further reading... er... watching:
• How Big are All Infini...
• A Hierarchy of Infinit...
• Defining Infinity | In...
Cantor portrait from Wikipedia: en.wikipedia.org/wiki/Georg_C...
Do you also miss Kelsey? Here's her new channel, Chalk Talk: @chalktalkmath
Do you also miss Tai-Danae? Her blog Math3ma is still up, now with a companion podcast:
www.math3ma.com/ and • The fAQ on fAQ - ep 00
I sadly could not find Gabe still online anywhere. We still miss you!
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