I can write an algorithm that is capable of describing ('reaching') every possible irrational number - given infinite resources. The infinite is not a number-like object, it is an active form of incrementation or concatenation. So I can write an algorithm that can write *every* finite state of *every* possible number. However, it would take another algorithm to 'prove' it. Given an irrational number, this other algorithm could find the infinite incrementation for every digit of the given number. Each possible number (including the incrementation of those numbers that cannot be represented in truncated form) is embedded within a single infinite infinite incrementation of digits that is produced by the algorithm, so the second algorithm would have to calculate where you would find each digit of the given irrational number by increment. But the thing is, both functions would be computable and provable. (I haven't actually figured the second algorithm out yet, but it is not a difficult problem.)
This means that the Trans-Infinite Is Computable. But don't tell anyone about this, it's a secret. ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com