4 ms·
This is not an infinite decimal. The digit 1 is somewhere out there.
by jonsen 6y ago
This is not an infinite decimal. The digit 1 is somewhere out there.
- oconnor663 6y agoThough you could treat it as an infinite series in a similar way: 0.9 -> 0.99 -> 0.999 -> ... -> ? 0.1 -> 0.01 -> 0.001 -> ... -> ?
- jonsen 6y agoThe first is an infinite series: 9/10 + 9/100 + 9/1000 + ... + 9/10^n + ... The second is not?!
- deleted 6y ago[deleted]
- oconnor663 6y agoI mean you could if you want to: 1/10 + -9/100 + -9/1000 + -9/10000 + ... But I just meant them as series, not necessarily as sums.
- jonsen 6y agoOr 1 - 9/10 - 9/100 - ... or 1 - ( 9/10 + 9/100 + ... ) So it becomes circular: 0.00...1 = 1 - 0.999... (In math a series is a sum: https://en.m.wikipedia.org/wiki/Series_(mathematics) https://en.m.wikipedia.org/wiki/Series_(mathematics)
- oconnor663 6y agoWoops, you're totally right, I think I should've said "sequence".
- UncleMeat 6y agoBut this is not a compelling argument to somebody in this situation. While correct, it feels identical to saying "it just is".
- jdsully 6y agoThe whole numerical representation scheme really is just a man made system. If you dig deep enough the veneer disappears. This is especially noticeable when you start to see things like numbers that are finite in decimal but have infinite repeating patterns binary.