Talk:Existence of Base-N Representation

From ProofWiki
Jump to navigation Jump to search

This appears to be an extension of the Basis Representation Theorem but I don't have the time to go through it and compare it for details.

Would it be worth trying to put them into the same page, or would it be better to keep them separate? --prime mover 05:17, 8 September 2010 (UTC)

A merge isn't wise. For one thing, the basis representation theorem states there is a finite expansion for an integer in terms of positive powers of another, and that the expansion is unique. This theorem states there is a (not necessarily finite) expansion for any real number in [0,1), in terms of negative powers of an integer, and that this expansion is unique if and only if the expansion does not naturally terminate.
Together, the two theorems demonstrate a base-p "decimal" expansion for ANY real number, but they are very different theorems. J D Bowen 05:21, 8 September 2010 (UTC)
Fair enough ... so what we can then do is provide a separate page to combine the result and so justify the representation of any real number. All good stuff. --prime mover 05:26, 8 September 2010 (UTC)