Thanks to Raul, Roger, and Oleg for your replies. Roger Hui wrote:
> The Wikipedia article makes a distinction between > a=b (mod c) and a≡b (mod c) . I have not run > across any situations where this distinction is > necessary, because to me both are readily under- > standable and correct (and equivalent). I agree. The distinction drawn there seems neither useful nor clear. My confusion is something I can reduce by using J, another case where notation serves as a tool of thought. Reading that paragraph I did not have a clear sense of the difference asserted between congruence and equality in modular arithmetic, but if I can write them in J that difference will be clear. That won't resolve *why* the distinction has been made, however. I greatly like the verb Raul posted, em, for it neatly applies the relationship of modular congruence through array-oriented thinking. Oleg's conjunction was engaging first because of how it relies on parentheses to come closer to standard math notation, and because of the thought process that occurred when I tried to extend that to match conventional notation completely. This cannot occur, I think, because the target notation requires a number at the far left and not at the far right. Regardless, the strengths of J are not in matching standard notation (where Mathematica strives to be strong) but rather in consistency and extensibility. Thus I now think my verbs (cgt and meq) are backwards from what they should be. The J standard of control-verb-data should be followed given that I'm making J the notation. Having written the above, I have discovered Devon's reply on this topic and found it particularly useful. The distinction in question is now clear to me. Devon's version of cgt is a noticeable improvement, especially because it permits simple array use as he said. But also, the use of 1=#~.n as a technique for testing equality is one I want to remember. Thank you, Devon. -- Tracy ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
