numbers near machine precision

*To*: mathgroup at smc.vnet.net*Subject*: [mg47049] numbers near machine precision*From*: Steve Story <sbstory at ncsu.edu>*Date*: Mon, 22 Mar 2004 00:15:01 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I'm in a numerical methods class, and having difficulty adapting the subroutines to Mathematica. For one thing, it seems that the == operator will pronounce two numbers equal when they're much further apart than machine epsilon. And I don't understand why this is, but it's easy to work around for the routines I'm using. A bigger problem, however, is that when I try to look at a machine-precise number in different number systems, sometimes Mathematica says they're identical, sometimes not. And I can't find a good resource about this. This problem is much more confusing to me. Here's an example which I can't explain. In the first case, they're not identical, in the second, they are: In[132]:= RealDigits[{a,b},2] Out[132]= {{{1,0,0,1,0,0,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,1,1,1,1,1,0, 1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0},2},{{1,0,0,1,0,0,0,1,1,0,1,1,1,1,1,0,1, 0,0,1,0,1,0,0,1,0,1,0,0,1,1,1,1,1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0, 1},2}} In[135]:= RealDigits[{a,b},16] Out[135]= {{{2,4,6,15,10,5,2,9,15,13,11,3,3},1},{{2,4,6,15,10,5,2,9,15,13,11,3,3},1}} I don't understand why those things are happening in Mathematica. If anyone could point me to a deep discussion of these topics in Mathematica, I'd appreciate it. thanks, Steve Story