Help with a simple group theory question please

[Ineedhelpimbadatphys]

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

above

 

[fresh_42]

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

above

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\}##.