You are welcome to define and implement a system where relative tolerance is permitted to be greater than 1. As for me, a concept of equality which is meaningless for a significant subdomain, viz. the non-negative real numbers, is meaningless enough for me.
Well, I haven't defined "significant" either, and I am not going to; I just know what it is when I see it. I also know that this discussion is fast becoming not it. ----- Original Message ----- From: "Oleg Kobchenko" <[EMAIL PROTECTED]> To: "Programming forum" <[email protected]> Sent: Tuesday, May 30, 2006 12:51 PM Subject: Re: [Jprogramming] Equal tolerance fit conjunction -- again You are considering only part of the domain (points with the same direction) -- is that part of the requirement for "meaningful"? Then it needs to be stated. Otherwise, less casual experimentation reveals that 1 looks like a smooth transition from similar neighboring states. Whereas 2 gives a breaking point. ((0.6 teq)"0/~ ; (1 teq)"0/~; (1.4 teq)"0/~) i:6 +-------------------------+-------------------------+-------------------------+ |1 1 1 1 0 0 0 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 0|1 1 1 1 1 1 1 1 1 0 0 0 0| |1 1 1 1 1 0 0 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 0|1 1 1 1 1 1 1 1 1 0 0 0 0| |1 1 1 1 1 0 0 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 0|1 1 1 1 1 1 1 1 0 0 0 0 0| |1 1 1 1 1 0 0 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 0|1 1 1 1 1 1 1 1 0 0 0 0 0| |0 1 1 1 1 1 0 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 1 1| |0 0 0 0 1 1 0 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 1 1 1 1| |0 0 0 0 0 0 1 0 0 0 0 0 0|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |0 0 0 0 0 0 0 1 1 0 0 0 0|0 0 0 0 0 0 1 1 1 1 1 1 1|1 1 1 1 0 0 1 1 1 1 1 1 1| |0 0 0 0 0 0 0 1 1 1 1 1 0|0 0 0 0 0 0 1 1 1 1 1 1 1|1 1 0 0 0 0 1 1 1 1 1 1 1| |0 0 0 0 0 0 0 0 1 1 1 1 1|0 0 0 0 0 0 1 1 1 1 1 1 1|0 0 0 0 0 1 1 1 1 1 1 1 1| |0 0 0 0 0 0 0 0 1 1 1 1 1|0 0 0 0 0 0 1 1 1 1 1 1 1|0 0 0 0 0 1 1 1 1 1 1 1 1| |0 0 0 0 0 0 0 0 1 1 1 1 1|0 0 0 0 0 0 1 1 1 1 1 1 1|0 0 0 0 1 1 1 1 1 1 1 1 1| |0 0 0 0 0 0 0 0 0 1 1 1 1|0 0 0 0 0 0 1 1 1 1 1 1 1|0 0 0 0 1 1 1 1 1 1 1 1 1| +-------------------------+-------------------------+-------------------------+ ((1.6 teq)"0/~ ; (2 teq)"0/~; (2.4 teq)"0/~) i:6 +-------------------------+-------------------------+-------------------------+ |1 1 1 1 1 1 1 1 1 1 0 0 0|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 1 1 1 1 1 0 0 0|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 1 1 1 1 0 0 0 0|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 1 1 1 0 0 0 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 1 1 1 0 0 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 1 1 0 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 0 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 0 0 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 0 0 0 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |0 0 0 0 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |0 0 0 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |0 0 0 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| +-------------------------+-------------------------+-------------------------+ --- Roger Hui <[EMAIL PROTECTED]> wrote: > Evidently you don't consider that > > 1 (1 teq) 1e9 > 1 > > is not a "meaningful result". Even casual further experimentation > produces: > > 1 (1 teq) 0 1 2 3 4 5 6 > 1 1 1 1 1 1 1 > 1 teq"0/~ 10 [EMAIL PROTECTED] 1e6 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > > is that meaningless enough for you? ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
