confused about == vs === in this equality
in [Mathematica]
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From: Albert Retey on 9 Oct 2009 07:17 Drago Ganic wrote: > Hi Andrzej, > there is one function (Missing) and one symbol (Null) which >>should<< > behave the same as Indetereminate and ComplexInfinity but unfortunatly does > not. > > In[1]:= Null == Null > Out[1]= True > > In[2]:= Missing[] == Missing[] > Out[2]= True > > Null is Mathematica legacy which has basically the same meaning as Missing[] > (or maybe Missing["Nonexistent"]). Missing incorporates Indetereminate via > Missing["Indeterminate"]. Why would you call Null "Mathematica legacy"? AFAIK Missing is by no means meant to "replace" Null. From the documentation Missing is something that is returned by Datafunctions only while Null has much wider applications in the Mathematica language. Have you information that is beyond the documentation? > All of those (Indetereminate & ComplexInfinity for numeric data and > Null/Missing for any kind of data), are so called "null values" in database > systems and for them the Equal and other logical connectivities (And, Or, > Not, etc.) are overloaded. Unfortunatly this is not the case in Mathematica. While I think (but not yet am convinced) that this might make sense for Missing, I think Null is not that easily compared to a database null value and thus I would expect lots of problems and side effects if Null == Null would return False... just wondering... albert
From: Andrzej Kozlowski on 9 Oct 2009 07:17 Hi Drago, I have to say I am not convinced about Null (I have not thought about missing). My reason is simply this: in the case of Intermediate it is easy to construct two completely unrelated expressions which will evalute to Intermediate. Having Intermediate==Intermediate evaluate to True would lead to equality between these expressions also evaluating to True. Conceivably this could be "hidden" within some complicated computation and result in a totally misleading final result. On the other hand I don't know of anything but Null that *evaluates" to Null. If you can produce two obviously unrelated expressions both of which evaluate to Null then indeed I will agree with you. As it is I think the current situation is just fine. Andrzej On 8 Oct 2009, at 20:50, Drago Ganic wrote: > Hi Andrzej, > there is one function (Missing) and one symbol (Null) which >>should<< > behave the same as Indetereminate and ComplexInfinity but > unfortunatly does > not. > > In[1]:= Null == Null > Out[1]= True > > In[2]:= Missing[] == Missing[] > Out[2]= True > > Null is Mathematica legacy which has basically the same meaning as > Missing[] > (or maybe Missing["Nonexistent"]). Missing incorporates > Indetereminate via > Missing["Indeterminate"]. > All of those (Indetereminate & ComplexInfinity for numeric data and > Null/Missing for any kind of data), are so called "null values" in > database > systems and for them the Equal and other logical connectivities > (And, Or, > Not, etc.) are overloaded. Unfortunatly this is not the case in > Mathematica. > > Greetings from Croatia, > Drago Ganic > > "Andrzej Kozlowski" <akoz(a)mimuw.edu.pl> wrote in message > news:hacmoa$sko$1(a)smc.vnet.net... >> I amy be taking a bit of a risk here, but I would guess that >> ComplexInfinity and Indeterminate are the only symbols in Mathematica >> with this property, that is we get: >> >> a=ComplexInfinity >> >> TrueQ[Unevaluated[x == x] /. x -> a] >> >> False >> >> a = Indeterminate; >> >> TrueQ[Unevaluated[x == x] /. x -> a] >> >> False >> >> I believe that there are no other symbols for which this happens (?) >> (If I am right and it is the only one that there is no need to be >> seriously concerned or, as you say, "careful" about this issue.) >> >> Why does and Indeterminate and ComplexInfinity behave in this way? Of >> course this is a matter of design and not (for example) mathematics >> so >> the question really is, is this a reasonable and useful thing rather >> than if it is right. I guess it is pretty clear that since >> Indeterminate refers to a magnitude that cannot be determined, you >> would not really want to assert that two expressions, both of which >> evaluate to Indeterminate, are in any sense equal. For example it >> would seem very strange if >> >> Infinity - Infinity == Infinity/Infinity >> >> returned True (as would have to be the case if >> Indeterminate==Indeterminate returned True). Similar considerations >> perhaps apply to ComplexInfinity, which refers to a complex quantity >> with infinite magnitude but with an indeterminate argument. (However, >> I am less convinced of that in the case of ComplexInfinty than in the >> case of Indeterminate, because ComplexInfinity has a natural >> interpretation as a unique point on the Riemann sphere). >> >> (Of course === asks quite a different question and there is no doubt >> that when you have identical expressions on both sides of === the >> answer should always be True.) >> >> Andrzej Kozlowski >> >> >> >> >> >> >> On 4 Oct 2009, at 18:35, Nasser Abbasi wrote: >> >>> ?=== >>> lhs===rhs yields True if the expression lhs is identical to rhs, and >>> yields >>> False otherwise. >>> >>> ?== >>> lhs==rhs returns True if lhs and rhs are identical. >>> >>> But looking at this example: >>> >>> a = ComplexInfinity; >>> If[a == ComplexInfinity, Print["YES"]] >>> >>> Expecting it would print "YES", but it does not. it just returns the >>> whole >>> thing unevaluated? But >>> >>> If[a === ComplexInfinity, Print["YES"]] >>> >>> does return YES. >>> >>> I guess I am a little confused about the "expression" bit in the >>> definition. >>> >>> So, when using the 3"=", it is looking at the _value_ of the >>> expression, but >>> when using the 2"=", it is looking at the expression _as it is_, >>> i.e. >>> without evaluating it? Is this the difference? I've always used >>> the 2"=" >>> for equality, now I have to be more careful which to use. >>> >>> --Nasser >>> >>> >>> __________ Information from ESET NOD32 Antivirus, version of virus >>> signature database 4478 (20091003) __________ >>> >>> The message was checked by ESET NOD32 Antivirus. >>> >>> http://www.eset.com >>> >>> >>> >>> >> >> > >
From: Andrzej Kozlowski on 9 Oct 2009 07:19 In my post below I wrote "missing" instead of "Missing" and "Intermedite" instead of "Indeterminante" (3 times!) How much more mindless can one get? Andrzej On 9 Oct 2009, at 11:14, Andrzej Kozlowski wrote: > Hi Drago, > > I have to say I am not convinced about Null (I have not thought > about missing). My reason is simply this: in the case of > Intermediate it is easy to construct two completely unrelated > expressions which will evalute to Intermediate. Having > Intermediate==Intermediate evaluate to True would lead to equality > between these expressions also evaluating to True. Conceivably this > could be "hidden" within some complicated computation and result in > a totally misleading final result. > > On the other hand I don't know of anything but Null that *evaluates" > to Null. If you can produce two obviously unrelated expressions both > of which evaluate to Null then indeed I will agree with you. As it > is I think the current situation is just fine. > > Andrzej > > > On 8 Oct 2009, at 20:50, Drago Ganic wrote: > >> Hi Andrzej, >> there is one function (Missing) and one symbol (Null) which >> >>should<< >> behave the same as Indetereminate and ComplexInfinity but >> unfortunatly does >> not. >> >> In[1]:= Null == Null >> Out[1]= True >> >> In[2]:= Missing[] == Missing[] >> Out[2]= True >> >> Null is Mathematica legacy which has basically the same meaning as >> Missing[] >> (or maybe Missing["Nonexistent"]). Missing incorporates >> Indetereminate via >> Missing["Indeterminate"]. >> All of those (Indetereminate & ComplexInfinity for numeric data and >> Null/Missing for any kind of data), are so called "null values" in >> database >> systems and for them the Equal and other logical connectivities >> (And, Or, >> Not, etc.) are overloaded. Unfortunatly this is not the case in >> Mathematica. >> >> Greetings from Croatia, >> Drago Ganic >> >> "Andrzej Kozlowski" <akoz(a)mimuw.edu.pl> wrote in message >> news:hacmoa$sko$1(a)smc.vnet.net... >>> I amy be taking a bit of a risk here, but I would guess that >>> ComplexInfinity and Indeterminate are the only symbols in >>> Mathematica >>> with this property, that is we get: >>> >>> a=ComplexInfinity >>> >>> TrueQ[Unevaluated[x == x] /. x -> a] >>> >>> False >>> >>> a = Indeterminate; >>> >>> TrueQ[Unevaluated[x == x] /. x -> a] >>> >>> False >>> >>> I believe that there are no other symbols for which this happens (?) >>> (If I am right and it is the only one that there is no need to be >>> seriously concerned or, as you say, "careful" about this issue.) >>> >>> Why does and Indeterminate and ComplexInfinity behave in this way? >>> Of >>> course this is a matter of design and not (for example) >>> mathematics so >>> the question really is, is this a reasonable and useful thing rather >>> than if it is right. I guess it is pretty clear that since >>> Indeterminate refers to a magnitude that cannot be determined, you >>> would not really want to assert that two expressions, both of which >>> evaluate to Indeterminate, are in any sense equal. For example it >>> would seem very strange if >>> >>> Infinity - Infinity == Infinity/Infinity >>> >>> returned True (as would have to be the case if >>> Indeterminate==Indeterminate returned True). Similar considerations >>> perhaps apply to ComplexInfinity, which refers to a complex quantity >>> with infinite magnitude but with an indeterminate argument. >>> (However, >>> I am less convinced of that in the case of ComplexInfinty than in >>> the >>> case of Indeterminate, because ComplexInfinity has a natural >>> interpretation as a unique point on the Riemann sphere). >>> >>> (Of course === asks quite a different question and there is no doubt >>> that when you have identical expressions on both sides of === the >>> answer should always be True.) >>> >>> Andrzej Kozlowski >>> >>> >>> >>> >>> >>> >>> On 4 Oct 2009, at 18:35, Nasser Abbasi wrote: >>> >>>> ?=== >>>> lhs===rhs yields True if the expression lhs is identical to rhs, >>>> and >>>> yields >>>> False otherwise. >>>> >>>> ?== >>>> lhs==rhs returns True if lhs and rhs are identical. >>>> >>>> But looking at this example: >>>> >>>> a = ComplexInfinity; >>>> If[a == ComplexInfinity, Print["YES"]] >>>> >>>> Expecting it would print "YES", but it does not. it just returns >>>> the >>>> whole >>>> thing unevaluated? But >>>> >>>> If[a === ComplexInfinity, Print["YES"]] >>>> >>>> does return YES. >>>> >>>> I guess I am a little confused about the "expression" bit in the >>>> definition. >>>> >>>> So, when using the 3"=", it is looking at the _value_ of the >>>> expression, but >>>> when using the 2"=", it is looking at the expression _as it is_, >>>> i.e. >>>> without evaluating it? Is this the difference? I've always used >>>> the 2"=" >>>> for equality, now I have to be more careful which to use. >>>> >>>> --Nasser >>>> >>>> >>>> __________ Information from ESET NOD32 Antivirus, version of virus >>>> signature database 4478 (20091003) __________ >>>> >>>> The message was checked by ESET NOD32 Antivirus. >>>> >>>> http://www.eset.com >>>> >>>> >>>> >>>> >>> >>> >> >> >
From: DrMajorBob on 9 Oct 2009 07:25 I always found it annoying that Null isn't treated as a value, in database tests for equality. So I'm glad Mathematica didn't go that way. Bobby On Thu, 08 Oct 2009 06:50:29 -0500, Drago Ganic <dganic(a)vodatel.net> wrote: > Hi Andrzej, > there is one function (Missing) and one symbol (Null) which >>should<< > behave the same as Indetereminate and ComplexInfinity but unfortunatly > does > not. > > In[1]:= Null == Null > Out[1]= True > > In[2]:= Missing[] == Missing[] > Out[2]= True > > Null is Mathematica legacy which has basically the same meaning as > Missing[] > (or maybe Missing["Nonexistent"]). Missing incorporates Indetereminate > via > Missing["Indeterminate"]. > All of those (Indetereminate & ComplexInfinity for numeric data and > Null/Missing for any kind of data), are so called "null values" in > database > systems and for them the Equal and other logical connectivities (And, Or, > Not, etc.) are overloaded. Unfortunatly this is not the case in > Mathematica. > > Greetings from Croatia, > Drago Ganic > > "Andrzej Kozlowski" <akoz(a)mimuw.edu.pl> wrote in message > news:hacmoa$sko$1(a)smc.vnet.net... >> I amy be taking a bit of a risk here, but I would guess that >> ComplexInfinity and Indeterminate are the only symbols in Mathematica >> with this property, that is we get: >> >> a=ComplexInfinity >> >> TrueQ[Unevaluated[x == x] /. x -> a] >> >> False >> >> a = Indeterminate; >> >> TrueQ[Unevaluated[x == x] /. x -> a] >> >> False >> >> I believe that there are no other symbols for which this happens (?) >> (If I am right and it is the only one that there is no need to be >> seriously concerned or, as you say, "careful" about this issue.) >> >> Why does and Indeterminate and ComplexInfinity behave in this way? Of >> course this is a matter of design and not (for example) mathematics so >> the question really is, is this a reasonable and useful thing rather >> than if it is right. I guess it is pretty clear that since >> Indeterminate refers to a magnitude that cannot be determined, you >> would not really want to assert that two expressions, both of which >> evaluate to Indeterminate, are in any sense equal. For example it >> would seem very strange if >> >> Infinity - Infinity == Infinity/Infinity >> >> returned True (as would have to be the case if >> Indeterminate==Indeterminate returned True). Similar considerations >> perhaps apply to ComplexInfinity, which refers to a complex quantity >> with infinite magnitude but with an indeterminate argument. (However, >> I am less convinced of that in the case of ComplexInfinty than in the >> case of Indeterminate, because ComplexInfinity has a natural >> interpretation as a unique point on the Riemann sphere). >> >> (Of course === asks quite a different question and there is no doubt >> that when you have identical expressions on both sides of === the >> answer should always be True.) >> >> Andrzej Kozlowski >> >> >> >> >> >> >> On 4 Oct 2009, at 18:35, Nasser Abbasi wrote: >> >>> ?=== >>> lhs===rhs yields True if the expression lhs is identical to rhs, and >>> yields >>> False otherwise. >>> >>> ?== >>> lhs==rhs returns True if lhs and rhs are identical. >>> >>> But looking at this example: >>> >>> a = ComplexInfinity; >>> If[a == ComplexInfinity, Print["YES"]] >>> >>> Expecting it would print "YES", but it does not. it just returns the >>> whole >>> thing unevaluated? But >>> >>> If[a === ComplexInfinity, Print["YES"]] >>> >>> does return YES. >>> >>> I guess I am a little confused about the "expression" bit in the >>> definition. >>> >>> So, when using the 3"=", it is looking at the _value_ of the >>> expression, but >>> when using the 2"=", it is looking at the expression _as it is_, i.e. >>> without evaluating it? Is this the difference? I've always used >>> the 2"=" >>> for equality, now I have to be more careful which to use. >>> >>> --Nasser >>> >>> >>> __________ Information from ESET NOD32 Antivirus, version of virus >>> signature database 4478 (20091003) __________ >>> >>> The message was checked by ESET NOD32 Antivirus. >>> >>> http://www.eset.com >>> >>> >>> >>> >> >> > > -- DrMajorBob(a)yahoo.com
From: Albert Retey on 10 Oct 2009 07:10 Hi, > In my post below I wrote "missing" instead of "Missing" and > "Intermedite" instead of "Indeterminante" (3 times!) How much more > mindless can one get? one could mistype the _both_ corrections :-) albert
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