3 ms·
Well, an interesting fact is that every nonzero rational number has two equal representations in some bases, e.g. 0.999...=1. Zero is then is the only rational
by falcor84 7y ago
Well, an interesting fact is that every nonzero rational number has two equal representations in some bases, e.g. 0.999...=1. Zero is then is the only rational number with just one representation.
https://en.wikipedia.org/wiki/0.999.. https://en.wikipedia.org/wiki/0.999...
- dorgo 7y agoähmm, no? Counterexample: 1/3 >every nonzero TERMINATING decimal has two equal representations
- falcor84 7y agoI mentioned "in some bases". In base 3, it's 0.1 and 0.0222...
- cgriswald 7y agoYou can represent 0 a countably infinite number of ways: 0 0.0 0.00 0.000 0.0000 ...
- falcor84 7y agoWell, the convention in maths is that we never add trailing zeros, since they wouldn't as any information. Unlike in other sciences, where they represent measurement precision.
- cgriswald 7y agoThe same is true of .999... and 1. In any case, it’s an artifact of how we represent numbers, not an property of the numbers themselves.