Finding Two Points in a Convex Set: Help Needed!

In summary, the conversation is about finding two points in a given convex set for which the line segment joining them goes outside the set. The person has graphed the function and found the convex set, but is unsure of how to find the two points. They have found some points, but the answer is still incorrect. They ask for help and are reminded to solve the inequalities before graphing the set.
  • #1
reefster98
5
0
I have two a convex set:

{(x1, x2): 1≤ ∣x1∣ ≤2, ∣x2−3∣ ≤ 2}

I have to find two points in the set for which the line segment joining the points goes outside the set. I have graphed the function and found my convex set. My question is, how do I find these two points? I have found various points in which the answer is still incorrect.

Please help me. Thank you in advanced.
 
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  • #2
reefster98 said:
I have two a convex set:

{(x1, x2): 1≤ ∣x1∣ ≤2, ∣x2−3∣ ≤ 2}

I have to find two points in the set for which the line segment joining the points goes outside the set. I have graphed the function and found my convex set. My question is, how do I find these two points? I have found various points in which the answer is still incorrect.

Please help me. Thank you in advanced.
Is that set convex? Before you graph it, you need to solve those inequalities.
 
  • #3
Thank you, I got the answer to that question.
 

1. How do you define a convex set?

A convex set is a set of points where any line segment connecting two points in the set lies entirely within the set. In other words, the set does not have any indentations or holes.

2. What is the importance of finding two points in a convex set?

Finding two points in a convex set is important in many applications, such as optimizing algorithms, solving optimization problems, and analyzing geometrical structures. It also helps in understanding the structure and properties of convex sets.

3. How do you find two points in a convex set?

To find two points in a convex set, you can use the following steps:

  1. Pick any two points in the set.
  2. Draw a line segment connecting the two points.
  3. Check if the line segment lies entirely within the set.
  4. If yes, then you have found the two points in the convex set.
  5. If not, then pick another two points and repeat the process until you find two points that satisfy the convex set property.

4. Can there be more than two points in a convex set?

Yes, there can be more than two points in a convex set. In fact, a convex set can have an infinite number of points.

5. What are some real-life examples of convex sets?

Some real-life examples of convex sets are a circle, a sphere, a cube, a pyramid, and a cone. These shapes have a smooth and continuous boundary, which satisfies the convex set property.

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