Infinite elements in the universal sets

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Discussion Overview

The discussion revolves around the possibility of creating Venn diagrams that represent sets with infinite elements. Participants explore the implications of using infinite sets in such diagrams, particularly in relation to the relationships between different sets.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants question whether it is feasible to create a Venn diagram where the elements are infinite, citing examples of infinite sets like odd numbers and specific sequences.
  • Others suggest that Venn diagrams can represent both finite and infinite sets, indicating that the circles can illustrate the relationships between these sets.
  • A participant notes that in the provided example, the set W appears to be a subset of V, which raises questions about the nature of the elements being infinite.
  • There is a discussion about the historical use of Venn diagrams by Venn himself for logical arguments, with a focus on whether they have been used for counting non-finite sets.

Areas of Agreement / Disagreement

Participants express differing views on the use of Venn diagrams for infinite sets, with no consensus reached on the feasibility or implications of such representations.

Contextual Notes

There are limitations regarding the definitions of infinite sets and the assumptions about their representation in Venn diagrams. The discussion does not resolve these uncertainties.

rcs1
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is it possible to make a venn diagram wherein the elements are infinite elements?

ex. V = { is the set of all odd numbers)
W = { 5, 15, 25, 45, 55,...}

thanks a lot
 
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rcs said:
is it possible to make a venn diagram wherein the elements are infinite elements?
ex. V = { is the set of all odd numbers)
W = { 5, 15, 25, 45, 55,...}
I have never seen it done.
 
rcs said:
is it possible to make a venn diagram wherein the elements are infinite elements?
All sets are infinite? The circles in a Venn diagram can denote finite or infinite sets. The circles show how the sets are related. In this case, it seems that W is a subset of V.
 
Evgeny.Makarov said:
All sets are infinite? The circles in a Venn diagram can denote finite or infinite sets. The circles show how the sets are related. In this case, it seems that W is a subset of V.
I agree that Venn himself used the diagrams for logical arguments.
But the OP said "the elements are infinite elements". I take that to mean some sort of counting.
Have you seem Venn's diagrams used for counting non-finite sets?
 

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