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Message |
Ismail
science forum beginner
Joined: 20 Jun 2006
Posts: 5
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 Posted: Tue Jun 20, 2006 12:06 pm Post subject:
union convex set is not convex
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Hey,
i have some question about convex set.
- union convex set is not convex, why!!
e.g Sx and Sy are convex set and not disjoint but i need to proof
that Sz = Sx U Sy is convex, i think so, it exist a Set S = Sx
intresection Sy
S include Sz, then S is convex.
- i want to definie a convex set but the elments are exp-function and
not a simpel point.!!
e.g X = {x_i = exp(t) | 0<t <1, t is discret } <==> X =
{x_0,x_1,...x_n}
can you help my.
mes salutationes
Ismail |
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William Elliot
science forum Guru
Joined: 24 Mar 2005
Posts: 1906
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| Posted: Tue Jun 20, 2006 12:46 pm Post subject:
Re: union convex set is not convex
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On Tue, 20 Jun 2006, Ismail wrote:
| Quote: | i have some question about convex set.
- union convex set is not convex, why!!
e.g Sx and Sy are convex set and not disjoint but i need to proof that
Sz = Sx U Sy is convex, i think so, it exist a Set S = Sx intresection
Sy S include Sz, then S is convex.
|
The x-axis and the y-axis are convex and aren't disjoint.
Yet the union of the x-axis with the y-axis isn't convex.
On the other hand, the intersection of two convex sets is
always convex, even if they're disjoint.
| Quote: | - i want to definie a convex set but the elments are exp-function and
not a simpel point.!!
e.g X = {x_i = exp(t) | 0<t <1, t is discret } <==> X =
{x_0,x_1,...x_n}
can you help my.
mes salutationes
Ismail
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Dave L. Renfro
science forum Guru
Joined: 29 Apr 2005
Posts: 570
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| Posted: Tue Jun 20, 2006 12:48 pm Post subject:
Re: union convex set is not convex
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Ismail wrote (in part):
| Quote: | Hey,
i have some question about convex set.
- union convex set is not convex, why!!
e.g Sx and Sy are convex set and not disjoint [...]
|
What about the union of two lines whose intersection
is a single point?
Dave L. Renfro |
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Ismail
science forum beginner
Joined: 20 Jun 2006
Posts: 5
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| Posted: Tue Jun 20, 2006 1:07 pm Post subject:
Re: union convex set is not convex
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William Elliot schrieb:
| Quote: | On Tue, 20 Jun 2006, Ismail wrote:
The x-axis and the y-axis are convex and aren't disjoint.
Yet the union of the x-axis with the y-axis isn't convex.
|
sorry ,to avoide any mistake
i mean with Sx a convex set
Sx={X| X inc R^n} e.g X = {x_i = exp(-t) | 0<t <1, t is discret
}
Sy {Y| Y inc R^n } e.g Y = {z_i = t exp(-t) | 0<t <1, t is discret
}
and not x-axis.
| Quote: | - i want to definie a convex set but the elments are exp-function and
not a simpel point.!!
e.g X = {x_i = exp(t) | 0<t <1, t is discret } <==> X =
{x_0,x_1,...x_n}
can you help my.
mes salutationes
Ismail
|
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| Back to top |
|
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Dave L. Renfro
science forum Guru
Joined: 29 Apr 2005
Posts: 570
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| Posted: Tue Jun 20, 2006 2:01 pm Post subject:
Re: union convex set is not convex
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Ismail wrote:
| Quote: | sorry ,to avoide any mistake
i mean with Sx a convex set
Sx={X| X inc R^n}
e.g X = {x_i = exp(-t) | 0<t <1, t is discret}
Sy {Y| Y inc R^n }
e.g Y = {z_i = t exp(-t) | 0<t <1, t is discret}
|
What does "inc" mean? What does it mean to say that
a real number between 0 and 1 "is discret"?
Dave L. Renfro |
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Virgil
science forum Guru
Joined: 24 Mar 2005
Posts: 5536
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| Posted: Tue Jun 20, 2006 7:04 pm Post subject:
Re: union convex set is not convex
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In article <1150805185.982913.53340@i40g2000cwc.googlegroups.com>,
"Ismail" <ism002@yahoo.com> wrote:
| Quote: | Hey,
i have some question about convex set.
- union convex set is not convex, why!!
e.g Sx and Sy are convex set and not disjoint but i need to proof
that Sz = Sx U Sy is convex, i think so, it exist a Set S = Sx
intresection Sy
S include Sz, then S is convex.
- i want to definie a convex set but the elments are exp-function and
not a simpel point.!!
e.g X = {x_i = exp(t) | 0<t <1, t is discret } <==> X =
{x_0,x_1,...x_n}
can you help my.
mes salutationes
Ismail
|
A union of convex sets need not even be connected, much less convex.
Consider the union of two disjoint closed intervals. |
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Ismail
science forum beginner
Joined: 20 Jun 2006
Posts: 5
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| Posted: Wed Jun 21, 2006 9:18 am Post subject:
Re: union convex set is not convex
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i mean with Sx a convex set
| Quote: | Sx={X| X inc R^n}
e.g X = {x_i = exp(-t) | 0<= t <= n, t is natural }
Sy {Y| Y inc R^n }
e.g Y = {z_i = t exp(-t) | 0<= t <= n, t is natural number }
What does "inc" mean? What does it mean to say that
inc = include
a real number between 0 and 1 "is discret"?
t is natural number |
merci |
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David C. Ullrich
science forum Guru
Joined: 28 Apr 2005
Posts: 2250
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| Posted: Wed Jun 21, 2006 11:53 am Post subject:
Re: union convex set is not convex
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On 20 Jun 2006 06:07:27 -0700, "Ismail" <ism002@yahoo.com> wrote:
| Quote: |
William Elliot schrieb:
On Tue, 20 Jun 2006, Ismail wrote:
The x-axis and the y-axis are convex and aren't disjoint.
Yet the union of the x-axis with the y-axis isn't convex.
sorry ,to avoide any mistake
i mean with Sx a convex set
Sx={X| X inc R^n} e.g X = {x_i = exp(-t) | 0<t <1, t is discret
}
|
Whatever that means, it certainly does no appear to be a convex set.
| Quote: | Sy {Y| Y inc R^n } e.g Y = {z_i = t exp(-t) | 0<t <1, t is discret
}
and not x-axis.
- i want to definie a convex set but the elments are exp-function and
not a simpel point.!!
e.g X = {x_i = exp(t) | 0<t <1, t is discret } <==> X =
{x_0,x_1,...x_n}
can you help my.
mes salutationes
Ismail
|
************************
David C. Ullrich |
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Ismail
science forum beginner
Joined: 20 Jun 2006
Posts: 5
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| Posted: Thu Jun 22, 2006 10:52 am Post subject:
Re: union convex set is not convex
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David C. Ullrich wrote:
| Quote: | On 20 Jun 2006 06:07:27 -0700, "Ismail" <ism002@yahoo.com> wrote:
William Elliot schrieb:
On Tue, 20 Jun 2006, Ismail wrote:
The x-axis and the y-axis are convex and aren't disjoint.
Yet the union of the x-axis with the y-axis isn't convex.
sorry ,to avoide any mistake
i mean with Sx a convex set
Sx={X| X inc R^n} e.g X = {x_i = exp(-t) | 0<t <1, t is discret
}
Whatever that means, it certainly does no appear to be a convex set.
Sy {Y| Y inc R^n } e.g Y = {z_i = t exp(-t) | 0<t <1, t is discret
}
and not x-axis.
- i want to definie a convex set but the elments are exp-function and
not a simpel point.!!
e.g X = {x_i = exp(t) | 0<t <1, t is discret } <==> X =
{x_0,x_1,...x_n}
can you help my.
mes salutationes
Ismail
************************
David C. Ullrich
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i have proof the set is convex, what is your reason |
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Marc Olschok
science forum Guru Wannabe
Joined: 02 May 2005
Posts: 182
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| Posted: Thu Jun 22, 2006 5:25 pm Post subject:
Re: union convex set is not convex
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Ismail <ism002@yahoo.com> wrote:
| Quote: | Hey,
i have some question about convex set.
- union convex set is not convex, why!!
|
Could you just provide the definition of "convex" that you are using?
In all variants I know of, it is not difficult to give examples
of two convex sets whose union is not convex, even if their intersection
is nonempty.
Also note, that the actual statement "the union of convex sets is in general
not convex" does allow examples of the union of two convex sets being convex
again; it only states, that you cannot expect this to hold all the time.
Marc |
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