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- Explain how .3 repeating contains every possible digit. From where I'm looking, it can only contain the digit 3 by definition and therefore by definition cannot contain all of the possible digits.
- Consider this experiment - I toss a coin n times, where the nth toss is the first heads. Obviously, the possible values of n is the set of natural numbers 1, 2, 3, ... The probability of rolling a certain n=c, where c > ~20, becomes absurdly small, and approaches zero as c increases. However, it is completely possible to never toss a heads. Many people argue at this point that the probability of not tossing heads for even 30 tosses is already so close to zero that it might as well be zero. That is incorrect - since each toss is independant, I have a 1/2 chance of tossing heads in each case, regardless of how many times I have tossed the coin. So I could continue to toss tails forever.
- Therefore, to assume that infinity implies that everything that could possibly exist or happen does in fact exist or happen is not concrete.
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Sure I have a heart; it's floating in a jar in my closet, along with my tonsils, my appendix, and all of the other useless organs I ripped out.
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