tag:blogger.com,1999:blog-3993498847203183398.post3522121728417479941..comments2022-01-19T22:15:45.184+00:00Comments on RevK<sup>®</sup>'s ramblings: Irrational numbers and copyrightRevKhttp://www.blogger.com/profile/12369263214193333422noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3993498847203183398.post-65381792235776496322022-01-05T11:43:22.998+00:002022-01-05T11:43:22.998+00:000.2 is infinitely recurring when written in base-2...0.2 is infinitely recurring when written in base-2 but simple to write in base-10. Therefore you can "add something to the end" of all rational numbers by representing them in the "correct" base.<br /><br />It might be useful to represent numbers as a series of Continued Fractions rather than in a particular base. I used a similar representation in an encoder I wrote that can represent *any* rational number in such a way that if you lexicographically sort numbers in that representation you end up with them sorted numerically.<br /><br />andyjpbhttps://www.blogger.com/profile/07760004454338857872noreply@blogger.comtag:blogger.com,1999:blog-3993498847203183398.post-81238901905491043982021-12-27T14:28:09.378+00:002021-12-27T14:28:09.378+00:00Liouville's number is a beautiful thing, creat...Liouville's number is a beautiful thing, created by description: <br />https://www.youtube.com/watch?v=c9nUAXUSuII<br /><br />But if you're really uncomfortable with numbers created by description, then you're heading into territory inhabited by only a rather strange minority of mathematicians, and you'll have to face the consequences. If, for example, you extend the arguments of someone like Norman Wildberger, you might end up having to exclude not only the irrationals but also the rationals beyond some arbitrary denominator.<br />It all boils down to what you mean by "exist". The philosophy of numbers includes various interpretations: Platonism, constructivism, formalism, etc. It's an absorbing rabbit-hole to explore...Grahamhttps://www.blogger.com/profile/08886928382850688901noreply@blogger.comtag:blogger.com,1999:blog-3993498847203183398.post-35357371841571398452021-12-26T08:16:07.839+00:002021-12-26T08:16:07.839+00:00Feels like you've got this going on
https://w...Feels like you've got this going on<br /><br />https://www.youtube.com/watch?v=mZBwsm6B280Anonymousnoreply@blogger.com