The discussion centers on the union of sets in topology, specifically examining whether the union of the sets {∅, R} and {]a,∞[: a ∈ R} is equivalent to {∅, R}. It is established that the union results in a set containing three distinct elements: ∅, R, and {r | r > a}. This clarification emphasizes the importance of understanding the nature of set elements in topology.
PREREQUISITESStudents of mathematics, particularly those studying topology and set theory, as well as educators seeking to clarify concepts related to unions of sets.
Or is true. The elements of your sets are sets again. ##\emptyset\, , \,\mathbb{R}\, , \,\{r\,|\,r>a\}## are three sets, but here we consider them as the elements of ##\{\emptyset\, , \,\mathbb{R}\}## and ##\{(a,\infty )\}##. This makes the union a set with three elements, ##\emptyset\, , \,\mathbb{R}\, , \,\{r\,|\,r>a\}##.Ineedhelpimbadatphys said:Homework Statement: the question is about topology, but i just want to know.
isn't {∅,R}∪{]a,∞[:a∈R} equal to {∅,R}
since every member of {]a,∞[:a∈R} is a real number?
or am i just completely misunderstanding unions and intersections?
Relevant Equations: above
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