3 ms·
Binary is the only base where that proof does not work well easily, because 100000... = 011111... in a metric system.
by hgsgm 4y ago
Binary is the only base where that proof does not work well easily, because 100000... = 011111...
in a metric system.
- IIAOPSW 4y ago100000... is only equal to 011111... if your digits roll over, but if your digits roll over then you have a p-adic number system (specifically a 2-adic system), and the exact same argument would hold equally well for the 10-adic applied to 10000..... = 99999..... You argument isn't dependent on being binary or not. Only that the numbers roll over.
- Dylan16807 4y agoIn bases higher than 2, you can avoid the issue entirely by saying that some digits get +1 and other digits get -1. If the generated number only has digits 1-8, then 0000... vs 9999... is obviously not a problem.
- deleted 4y ago[deleted]