MHB What is the concept of limiting event?

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The concept of a limiting event relates to the definitions of sets and intervals in mathematical analysis. Members of the math help board are asked to provide clear explanations and examples for specific highlighted points regarding limiting events. It is noted that the definitions themselves do not require proof, as they are foundational concepts. The discussion also introduces the set ##E_k##, defined by the open interval ##( 1 - \frac{1}{2^k} , 2 + \frac{1}{2^k})##, which illustrates the idea of approaching a limit. Understanding limiting events is essential for grasping more complex mathematical principles.
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Would any member of math help board prove highlighted 1 and 2 by simple and clear explanation with examples?
 
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These are definitions, there is nothing to prove.
 
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WMDhamnekar said:
with examples?

Try letting ##E_k## be the set defined by the open interval ##( 1 - \frac{1}{2^k} , 2 + \frac{1}{2^k})##
 

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