Is the Union and Intersection of a Null Collection Valid in Set Theory?

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Discussion Overview

The discussion revolves around the validity of the union and intersection of a null collection of subsets in set theory. Participants explore definitions and implications related to these operations, examining both theoretical and conceptual aspects.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant cites a book stating that if C is the null collection of subsets of S, then the union of C is the null set and the intersection is S.
  • Another participant questions the definition of a null collection of subsets, implying that clarity on this definition is necessary for the discussion.
  • A participant references an external link to support their understanding of the definitions related to empty union and intersection.
  • One participant expresses skepticism about the claims but acknowledges that using the definition leads to a true statement.
  • Another participant presents an analogy comparing a null collection of sets to a game with no rules, suggesting that the intersection corresponds to all possible moves, which is the entire set S.
  • A participant reflects on their previous struggles with the same problem, indicating that the discussion may be helpful for others facing similar issues.
  • One participant reiterates the claims from the book, providing reasoning that supports the assertion that the union of C is the null set and the intersection is S, based on the absence of members in C.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and implications of the union and intersection of a null collection. While some find the definitions valid, others seek clarification and express skepticism, indicating that the discussion remains unresolved.

Contextual Notes

There is a reliance on specific definitions of a null collection, which may not be universally accepted. The discussion also reflects varying interpretations of the terms union and intersection in this context.

JasonRox
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The book that I'm reading is saying...

If C is the null collection of subsets of S then,

(Union) C = Null

(Disjoint) C = S

Is this true?
 
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How does your book define a null collection of subsets?
 
JasonRox said:
The book that I'm reading is saying...
If C is the null collection of subsets of S then,
(Union) C = Null
(Disjoint) C = S
Is this true?
Take it as a definition, or read this, for example:

http://at.yorku.ca/cgi-bin/bbqa?forum=ask_a_topologist_2004;task=show_msg;msg=0896.0001

since i presume by (disjoint) you actually mean intersection.

incidentally i got that answer by insertingf the words empty intersection into google and clicking the first link.

empty union requires you to follow the third (non indented) link.

you might want to remember that the next time you struggle to check a definition,
 
Last edited:
The truth is that I searched and searched. Then I thought and thought, then searched again.

Using the definition it is true, and I see that, but I was skeptical about it.

Thanks, for the link.
 
Last edited:
imagine a list of rules for a game which has no rules at all!

the intersection of a null collection of sets, corresponds to those moves which satisfy all the rules, hence any move at all, i.e. S.etc...you do the other case
 
JasonRox said:
The book that I'm reading is saying...
If C is the null collection of subsets of S then,
(Union) C = Null
(Disjoint) C = S
Is this true?

if x is in (Union)C, then it must be in at least one of the members of C. But C has no members so that is always false. Yes, (Union) C= Null set.

By (Disjoint) C do you mean the intersection[\b] of all the members of C?

Let x be any member of S. If x is NOT in (intersection) C, then there must be some member of C such that x is NOT in it. But that's NEVER true because C has no members! Therefore every member of S is in (Intersection) C.
 

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