I have a question that relates to this question about Venn diagrams. Has anyone shown that all Venn diagrams can (theoretically) be constructed?
Tell me more
×
Mathematics Stack Exchange is a question and answer site for
people studying math at any level and professionals in related fields. It's 100% free, no registration required.
|
|
There is a recursive construction for Venn diagrams (see the wikipedia page for Venn Diagram), so by induction there is a Venn diagram for any finite $n$. For $n\approx\omega$, it is more complicated, since $2^\omega\approx\mathbb R$, but I think it can be done. But if $n\succ\omega$, then $2^n\succ\mathbb R^2$, so it can definitely not be done on a plane (because there simply aren't enough points on the plane to do the job). |
|||
|
|
