Path: csiph.com!aioe.org!.POSTED!not-for-mail From: Daniel Bastos Newsgroups: comp.programming Subject: Re: on expressing o() in terms of O(), Omega() or Theta() Date: Mon, 20 Mar 2017 15:44:30 -0300 Organization: Aioe.org NNTP Server Lines: 19 Message-ID: <86pohbn5yp.fsf@toledo.com> References: <86var4n9nc.fsf@toledo.com> <20170319200229.778@kylheku.com> NNTP-Posting-Host: BuEqJTf8bEmpZhBIUMG+Zw.user.gioia.aioe.org Mime-Version: 1.0 Content-Type: text/plain X-Complaints-To: abuse@aioe.org User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/24.3 (windows-nt) X-Notice: Filtered by postfilter v. 0.8.2 Cancel-Lock: sha1:dinDU6MaGwgOBUHg4xME9OrtgsU= Xref: csiph.com comp.programming:7591 Kaz Kylheku <336-986-7787@kylheku.com> writes: > On 2017-03-19, Daniel Bastos wrote: >> Is it possible to *define* o() in terms of O(), Omega() or Theta() --- or >> any combination of them? > > To warm up, first define <= and >= in terms of =. I don't think that's very easy to do. Don't think that I'm mathematically inclined, but I happen to have a book called The Structure of the Real Number System by Cohen and Ehrlich in which they define an order in N in Theorem 1.13. That's difficult work. I don't think I could understand that without a lot of work. But perhaps I get your point. The same strategy could be applied to the original question. That's a difficult exercise then! Thanks for pointing that out to me. I had no idea until now. Thank you.