Find roster form of the given Set

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SUMMARY

The discussion centers on the mathematical concept of expressing the set B = {(x,y): y = e^x, x ∈ ℝ} in roster form. Participants clarify that roster form requires listing all members of a set, but due to the uncountable nature of the set defined by the exponential function, it is impossible to list all elements. The conversation emphasizes the distinction between countable and uncountable sets, with roster form being applicable only to countable sets.

PREREQUISITES
  • Understanding of set theory and notation
  • Familiarity with the concept of countable vs. uncountable sets
  • Basic knowledge of functions, specifically exponential functions
  • Mathematical notation for expressing sets
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  • Study the properties of countable and uncountable sets
  • Learn about different methods of representing sets, including set-builder notation
  • Explore the implications of uncountability in real analysis
  • Investigate the characteristics of exponential functions and their graphs
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Let B be the non empty sets,
B ={(x,y):y = e^x, x belongs to set of real numbers}
Write the set in roster form.
 
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By "roster form" you mean a listing of all members, right? You understand there are not only an infinite number but an uncountable number of members in this set, don't you. So you cannot "list" them even in principle (as, for example, {(1, 1), (2, 4), (3, 9), ...}). That's pretty much what "uncountable" means.
 
@Hallsoflvy Yes roster method means to list all the element in curly brackets.
 

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