Question

Give an example of a set $A \subset \mathbf{R}^2$ for which $2 A \subset A+A$ but $2 A \neq$ $A+A$.

   Give an example of a set $A \subset \mathbf{R}^2$ for which $2 A \subset A+A$ but $2 A \neq$ $A+A$.

Competitive Equilibrium: Theory and Applications

Competitive Equilibrium: Theory and Applications

Bryan Ellickson 1st Edition

Chapter 1, Problem 12

Instant Answer

Step 1

$2A$ is the set of all points that can be obtained by multiplying every point in $A$ by 2. In other words, if $(x,y) \in A$, then $(2x,2y) \in 2A$. $A+A$ is the set of all points that can be obtained by adding every point in $A$ to every other point in $A$. In Show more…

Show all steps

lock

Thanks for your feedback!

Give an example of a set $A \subset \mathbf{R}^2$ for which $2 A \subset A+A$ but $2 A \neq$ $A+A$.

Play audio

Feedback

Powered by NumerAI

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later