I am just making a note for completeness. There are plenty of meaningless results for tolerances t<1 on positive real half-axis. In fact, for any N>1 there exists t<1 such that for all 1<:x<:N, 1<:y<:N it will produce meaningless results. Such t can be (N-1)%N.
1 ((%~ <:)1e10) teq 1e10 1 1 ((%~ <:)1e10) teq 1e11 0 1 ((%~ <:)(x:1e19)) teq x:1e19 1 1 ((%~ <:)(x:1e19)) teq >:x:1e19 0 --- Roger Hui <[EMAIL PROTECTED]> wrote: > 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 > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
