I like paradoxes but I can’t wrap my head around the Richard’s paradox.
In: Mathematics
You make an infinite list of every possible sentence that can describe a number. put the list in alphabetical order.
And then you announce a new number that is different from every number on the list because the 1st digit is off by one from the first digit of the first number, the second digit is off by one from the second digit of the second number, and so on.
You’ve now described a number that can’t be on the list of every possible sentences.
Therefore, such a list must be uncountably infinite.
This is a great video about what uncountably infinite means and how it connects to math, computers, and life: [https://www.youtube.com/watch?v=HeQX2HjkcNo&ab_channel=Veritasium](https://www.youtube.com/watch?v=HeQX2HjkcNo&ab_channel=Veritasium)
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