Proving Elements of a Set are Distinct

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Discussion Overview

The discussion revolves around the assumption of distinctness of elements within a set, specifically in the context of a proof involving the set {0,1,a,b}. Participants explore whether it is standard to consider all elements as distinct when they are explicitly listed in a question.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions whether it is assumed that all elements of a set are distinct when they are explicitly listed, noting that this assumption is crucial for their proof.
  • Another participant asserts that if a set is defined with particular elements, then those elements are distinct, suggesting a common convention.
  • A different reply emphasizes that conventions may vary and advises the original poster to consult their professor to clarify this assumption.

Areas of Agreement / Disagreement

There is no consensus on the assumption of distinctness; while some participants support the idea that listed elements are distinct, others caution against making this assumption without confirmation.

JG89
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If a question asks me to prove something about the elements of a set, say {0,1,a,b}, then is it assumed that all elements are distinct?

Because I am attempting a proof, but the only way to prove the proposition is if all elements are distinct. However, it doesn't say in the original question that all elements are distinct, which leads me to my question.
 
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JG89 said:
If a question asks me to prove something about the elements of a set, say {0,1,a,b}, then is it assumed that all elements are distinct?

Because I am attempting a proof, but the only way to prove the proposition is if all elements are distinct. However, it doesn't say in the original question that all elements are distinct, which leads me to my question.

Hi JG89! :smile:

Yes, if an exam question defines a set as including particular elements, then they are all distinct. :smile:
 
Last edited:
Thanks :)
 
tiny-tim said:
Hi JG89! :smile:

Yes, if an exam question defines a set as including particular elements, then they are all distinct. :smile:
Conventions vary. The OP ought to ask his professor before making such a dangerous assumption.
 

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