Would the cardinality of a set S = {a, b, {c, d}} be 5?

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Discussion Overview

The discussion revolves around the cardinality of the set S = {a, b, {c, d}} and whether it can be considered to have a cardinality of 5. Participants explore the definitions and implications of set membership and subsets.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions whether the cardinality of the set S is 5.
  • Another participant asserts that the cardinality is 3, identifying the elements as a, b, and {c, d}.
  • A further contribution suggests that if H = {c, d} and H is an element of S, then it raises questions about the membership of c and d in S, potentially implying a greater cardinality.
  • Another participant clarifies that H is an element of S, not a subset, which may affect the interpretation of cardinality.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the cardinality of the set, with competing views on the implications of set membership and subset relationships remaining unresolved.

Contextual Notes

Discussion includes nuances regarding set membership versus subset relationships, which may affect interpretations of cardinality.

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Would the cardinality of a set S = {a, b, {c, d}} be 5?
 
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Gear300 said:
Would the cardinality of a set S = {a, b, {c, d}} be 5?

No, 3. The elements of the set are a, b, and {c,d}.
 


some_dude said:
No, 3. The elements of the set are a, b, and {c,d}.

But let us say that H = {c,d}. Then S = {a, b, H}. Shouldn't it be so that if H ⊂ S, c ϵ H, and d ϵ H, then c ϵ S and d ϵ S...which would mean that you could pull out more than 3 elements out of S (unless it is improper to associate elements of a particular element of a set to that set).
 
Last edited:


H ϵ S, not H ⊂ S
 


I see...Thanks for the replies.
 

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