Comments by "Christian Baune" (@programaths) on "Mathologer" channel.

  1. 2 is an odd prime number because it's even.
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  2. Divergent and convergent series. Things everyone know when they are 10, but forgot because it's maths :-D
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  3. 20:23 No, because we ask the simplest answer. So, if you have "1,2,3,4, ?, ..." then you would say 5 and not 64, because you need less information to describe the sequence with 5 than the one with 64.
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  4. 23:01 is trivial to demonstrate. If you write numbers in binary on n positions, you will have n numbers with 1 ones, n chose 2 numbers with 2 ones, n chose 3 numbers with 3 ones etc. Here are 3 digit binary numbers: 000 001 010 100 101 110 111 You can indeed see that the "1" represent a chosen position, hence the total number of binary numbers on n position is given by the sum of C(n,i) for i=0 to n. Obviously, you've 2^n binary numbers on n positions. So, you just equated a sum to 2^n.
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