Are Unbounded Sets Always Unbounded When Combined?

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SUMMARY

The discussion centers on the mathematical concept of combining unbounded sets. It is established that the sum of two arbitrary unbounded sets, defined as A + B = {x + y | x ε A and y ε B}, results in another unbounded set. This conclusion is based on the properties of real numbers and the behavior of unbounded sets under addition.

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peace-Econ
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If an arbitrary unbounded set + another arbitrary unbounded set, is it also going to be an unbounded set?
 
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Sounds reasonable.
 
What does a set + another set mean? Do you mean the sets have real numbers and

A+B = {x+y| x ε A and y ε B}

or something else?
 

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