In our Science fiction, science fact project we asked you which question from the frontiers of physics you'd most like to see answered on Plus. We have just closed the poll and with nearly 20% of your vote the winning question is Does infinity exist?. We will now go off to talk to experts on the topic, and you'll see some answers in a package of articles and podcasts to be published soon.
In our two previous polls the winning questions were What is time? and Is there free will?. You can find some answers by clicking on the links.
Meanwhile, keep voting to tell us which question you would like us to answer next!
The Science fiction, science fact project is a collaboration between Plus and FQXi, an organisation that supports and disseminates research on questions at the foundations of physics and cosmology. The FQXi community website does for physics and cosmology what Plus does for maths: provide the public with a deeper understanding of known and future discoveries in these areas, and their potential implications for our worldview.
Infinity
I suggest that your article "A Glimpse of Cantor's Paradise" contains a semantic paradox. In your "Origins of Proof" you show that 1=2 by the expedient of division by zero! Cantor shows that different sets can be of different sizes, this is then used to suggest different infinities. But by definition a set has bounds and infinity has no bounds. So no set can be infinite no matter how large and the infinite contains all sets, indeed everything. I suggest that the finite is bounded by all that one can imagine and that the infinite is beyond ones imagination. So if you can imagine it, it is finite even if impossible.