When I started reading the proof I thought it was a mistake, a mismatch between the theorem to proof and the linked proof. I didn't expect using Kolmogorov axioms to prove this kind of sums. I really enjoyed reading it. I just learned something new today, thanks!
It also wasn't immediately clear to me that this _is_ a valid sample space, the explanation in https://old.reddit.com/r/math/comments/18szn6y/anyone_use_pr... provides a more formal but still readable construction
I especially like the "finite" variant/version of the proof which reframes this as a counting/combinatorial proof instead of a probability-based one.
Why is that f(n - 1)?
def f(s):
assert(s[0] == 'T')
return s[1:]
def f_inverse(s):
return 'T' + s def f(s):
assert(s[0] == 'H')
assert(s[1] == 'T') # can't be another H!
def f_inverse(s):
return 'HT' + s