Re: Re: equaltity of lists

*To*: mathgroup at smc.vnet.net*Subject*: [mg19139] Re: [mg19077] Re: equaltity of lists*From*: "David Park" <djmp at earthlink.net>*Date*: Thu, 5 Aug 1999 23:58:42 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Drago, But still, treating the objects as lists, and a and b as variables, you can't know if they are equal or not. But if you make a and b objects by making them strings Mathematica does return False. {"a", "b"} == {"b", "a"} False Or, if you really want to use symbols, you could use something like the following: SetAttributes[equal2, Listable]; equal2[a_Symbol, b_Symbol] := If[a === b, True, False] And @@ {a, b}~equal2~{b, a} False David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ >Hi there, > >Thanks for the answers, but I still have questions. > >1. I wanted to test the "objects" in a mathematical and not in > a structural way. Therefore I believe I have to use == (Equal) > not === (SameQ). > >2. My reasoning was as follows > (I'm not a mathematician so maybe it's wrong) > > In Mathematics the Set is a very basic way to collect some > objects together and treat them as one. In Mathematica the > same thing (only finite sets) is implemented with a list > with ONE difference: a list has an order and a Set has not. > (You can never implement something without order in the > computer - you can only neglect the order). > > So mathematically spoken > the set {a, b} IS EQUAL TO the set {b, a}. > > I can get this behavior in Mathematica if I write > Union[{b, a}] == Union[{a, b}] > True > > But when I tread the objects {a,b} and {b,a} as lists the > answer to the question should be false if we look at the > list as a supplement to the set in a mathematical way. > > Of course the same is with > > a == a > True > > and > > a == b > a == b > > or > > x == x^2 > x == x^2 > > Why not False? I don't see that this is only a structural > question ("use SameQ, don't use Equal and you will get False"). > The functions x and x^2 are mathematically not Equal, so an Equal > should return False (the case x=1 is not important for function > equality). Isn't a variable x just a function f (x) = x? > >3. Just another example > > Simplify[(x^2-1)/(x-1)] > 1+x > > But the two functions are not mathematically identical > (point x=1). > > When I try to plot the function > > Plot [(x^2-1)/(x-1),{x,-2,2}] > > I don't get the graph of the rational function (x^2-1)/(x-1). > Instead I get the graph of the linear function 1+x. > > When I ask > > Reduce [ (x^2-1)/(x-1) == 1 + x, x] > True > > What with x = 1 ? > > >Greetings >Drago Ganic > >P.J. Hinton <paulh at wolfram.com> wrote in message >news:Pine.LNX.4.10.9908030840160.1020-100000 at wabash.wolfram.com... >> On 2 Aug 1999, Drago Ganic wrote: >> >> > Hi !! >> > >> > Why don't I get an answer (False) when I ask Mathematica >> > >> > {a,b}=={b,a} >> > >> > like the one I get with >> > >> > {1,2}=={2,1} >> > False >> >> In order to get False as a result in your first example, you must use a >> stronger logical test function than Equal[]. You need to use SameQ[]. >> >> In[1]:= {a,b} === {b,a} >> >> Out[1]= False >> >> -- >> P.J. Hinton >> Mathematica Programming Group paulh at wolfram.com >> Wolfram Research, Inc. >> Disclaimer: Opinions expressed herein are those of the author alone. >> > > > >