MHB Prove: 2ε{a,2,b} in Set Theory

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The discussion centers on proving that 2 is an element of the set {a, 2, b} within axiomatic set theory. Participants seek clarity on the definitions of the set notation "{a, 2, b}" and the membership symbol "ε." The set is defined as the union of {a, 2} and {b}, which can be expressed as {a, 2} ∪ {b}. A reference to a similar problem and its solution is mentioned, but external links are discouraged. The conversation emphasizes the importance of understanding set definitions and notation in axiomatic set theory.
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Prove in any axiomatic set theory that:2ε{a,2,b} , where a,b are letters
 
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What is the definition of "{a, 2, b}" in "axiomatic set theory"? What is the definition of "ε"?
 
Country Boy said:
What is the definition of "{a, 2, b}" in "axiomatic set theory"? What is the definition of "ε"?

{a,2,b}={a,2}U{b}
 
solakis said:
{a,2,b}={a,2}U{b}
Or even better, starting from where you left off: [math]\{ a, 2 \} \cup \{ b \} = \left ( \{ a \} \cup \{ 2 \} \right ) \cup \{ b \}[/math]

-Dan
 
solakis said:
here is the solution for a similar problem given by seppel in MHF

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Please do not give a link to another site as a means of providing a solution, either by the author of the thread posted here, or by someone responding with a solution.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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