MHB Infinite elements in the universal sets

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Venn diagrams can represent both finite and infinite sets, illustrating their relationships. The discussion centers on whether it's possible to depict infinite elements within these diagrams. It is noted that the circles in a Venn diagram can still denote infinite sets, with one set potentially being a subset of another. The original poster's query about "infinite elements" suggests a focus on counting within these sets. The conversation highlights that while Venn diagrams are traditionally used for logical arguments, their application to non-finite sets remains less common.
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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