Prev: Docked cells and TagBoxNote / StatusArea
Next: OneStepTopReduction in System` Context in Mathematica 6+?
From: Jack L Goldberg 1 on 20 Mar 2010 03:47
Hi Folks,

Can anyone explain this:

In[1]:= Union[ 1 < x < 2, 3 < x < 5 ]

Out[1]= 5 < x

??

I am using a MacBook Pro, OS 10.6.2

Thanks,

Jack

From: rafscipio on 21 Mar 2010 03:05
On 20 Mar, 08:47, Jack L Goldberg 1 <jackg...(a)umich.edu> wrote:
> Hi Folks,
>
> Can anyone explain this:
>
> In[1]:= Union[ 1 < x < 2, 3 < x < 5 ]
>
> Out[1]= 5 < x
>
> ??
>
> I am using a MacBook Pro, OS 10.6.2
>
> Thanks,
>
> Jack

Hi,

As u can read on help of Union function in Generalization and
Extension par., "Union works with any head, not just List":

In[1]:= Union[f[a, x, b], f[c, x, d]]

Out[1]= f[a, b, c, d, x]

In your case, considering the internal representation of the
expressions, it results:

In[2]:= 1 < x < 2 // FullForm
Out[2]//FullForm= Less[1,x,2]

In[3]:= 3 < x < 5 // FullForm
Out[3]//FullForm= Less[3,x,5]

Hence using formula [1] the result of your union is equivalent to:

Less[1,2,3,5,x]

....and it's equivalent to 1<2<3<5<x
....and so to to 5<x

Scipione

From: DC on 21 Mar 2010 03:06
For a generic head f :

In[1]:= Union[f[x, y], f[y, w, z]]

Out[1]= f[w, x, y, z]

hence your result as FullForm[1<x<2]=Less[1,x,2].

Try

In[9]:= Union[Interval[{1, 2}], Interval[{3, 5}]]

Out[9]= Interval[{1, 2}, {3, 5}]

-Francesco

On 03/20/2010 07:47 AM, Jack L Goldberg 1 wrote:
> Hi Folks,
>
> Can anyone explain this:
>
> In[1]:= Union[ 1< x< 2, 3< x< 5 ]
>
> Out[1]= 5< x
>
> ??
>
> I am using a MacBook Pro, OS 10.6.2
>
> Thanks,
>
> Jack
>

From: Simon on 21 Mar 2010 03:07
Hi Jack,

that's pretty cool, but it comes from using Union where you shouldn't.
The full form for, say, 1<x<2 is Less[1,x,2]. Let's replace Less with
some unknown function f;

In[1]:= Union[f[1,x,2],f[3,x,5]]
Out[1]= f[1,2,3,5,x]

In[2]:= %/.f->Less
Out[2]= 5<x

So Union does two things - it joins to objects with the same head
together AND sorts their arguments into canonical order. For Less,
this doesn't really make sense.
Maybe you wanted to do something like:

In[3]:= Reduce[1<x<2&&3<x<5]
Out[3]= False

In[4]:= Simplify[1<x<2&&3<x<5]
Out[4]= False

Simon

On Mar 20, 3:47 pm, Jack L Goldberg 1 <jackg...(a)umich.edu> wrote:
> Hi Folks,
>
> Can anyone explain this:
>
> In[1]:= Union[ 1 < x < 2, 3 < x < 5 ]
>
> Out[1]= 5 < x
>
> ??
>
> I am using a MacBook Pro, OS 10.6.2
>
> Thanks,
>
> Jack


From: Chris Osborn on 21 Mar 2010 03:07
On Mar 20, 2:47 am, Jack L Goldberg 1 <jackg...(a)umich.edu> wrote:
> Hi Folks,
>
> Can anyone explain this:
>
> In[1]:= Union[ 1 < x < 2, 3 < x < 5 ]
>
> Out[1]= 5 < x
>
> ??
>
> I am using a MacBook Pro, OS 10.6.2
>
> Thanks,
>
> Jack

Hi Jack,

Union is usually applied to lists (expressions with head "List") like:

Union[ {3, 2, 1}, {4, 3} ] --> {1,2,3,4}

(it sorts the elements and removes duplicates).
If you apply it to inequalities it will treat the inequalities like
expressions with head "Less", e.g.:

Union[ Less[1, x, 2], Less[3, x, 5] ] --> Less[1, 2, 3, 5, x]

Here it has sorted the elements 1, x, 2, 3, 5, and x, and removed
duplicates.

The simplifier notices this is equivalent to:
Less[5, x]

or

5 < x

Chris

 |  Next  |  Last
Pages: 1 2 3
Prev: Docked cells and TagBoxNote / StatusArea
Next: OneStepTopReduction in System` Context in Mathematica 6+?