2 ms·

I don't get it. What does it mean that the last bit of Pi is 1 when there is no last digit?

• bartonfink 16y ago
  The clincher is that rightmost 0's after a decimal point are insignificant and can be discarded similarly to leftmost 0's before a decimal point. 00045.26030 = 45.2603 - the extra 0's are simply noise. In binary, the only non-0 digit is 1. This means that, if Pi does in fact terminate, its binary representation must terminate in a 1 - any 0's to the right of the last 1 carry no value. Now, that's a pretty big "if", but this isn't meant to be serious mathematics. It's just an interesting consequence of binary representation and the assumption that Pi might terminate, and is enough to make people do a bit of a double take when you phrase it along the lines of "the last bit of Pi [if it has one] is a 1".
  • cperciva 16y ago
    rightmost 0's ... which Pi doesn't have, since it has no rightmost bits at all... the last bit of Pi [if it has one] is a 1 This is true; it's also true that the last bit of Pi [if it has one] is a forty-two. A falsehood implies everything.