Prove: 2ε{a,2,b} in Set Theory

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Discussion Overview

The discussion revolves around proving the statement "2ε{a,2,b}" within the framework of axiomatic set theory. Participants explore the definitions and implications of the set notation and the membership relation.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests clarification on the definitions of "{a, 2, b}" and "ε" in the context of axiomatic set theory.
  • Another participant reiterates the definition of the set as "{a, 2} U {b}", suggesting a union of sets.
  • A further contribution expands on the union notation, presenting it as "\{ a, 2 \} \cup \{ b \} = \left ( \{ a \} \cup \{ 2 \} \right ) \cup \{ b \}".
  • One participant references a solution to a similar problem provided by another user, but does not elaborate on the solution itself.
  • Another participant emphasizes the guideline against linking to external sites for solutions, indicating a preference for self-contained discussions.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the definitions and implications of the terms used, and there is no consensus on the proof or the definitions involved.

Contextual Notes

Participants have not resolved the definitions of the set and membership relation, and there are references to external solutions that are not fully integrated into the discussion.

solakis1
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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

From our guidelines:

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.
 

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