A discussion on the Dialogue on Infinity blog on an exciting
topic: ” Is zero a anatural number?” led me to these comments
about zeroes and empty sets: Zero is not natural, even less so
is the empty set. A proof that any two empty sets are equal
usually involves the use of the outrageously infinitistic Axiom
of Extensionality. To many students in my Foundation Year course
(and they represent countries from Afghanistan to Zambia) a
proof of the uniquiness of THE empty set is a revelation — not
so much mathematical as linguistic, because for many of them
their native tongue has no definite article, or usage of
definite articles is different from that in English. In some
languages, definite articles can be used only to point a finger
to a concrete object and could be best translated not as “the”
but “that”. Try to say “take that empty set”. A few words for an
incidental Russian reader of this blog. A colleague of mine once
explained to me that in Russian regional dialects one can still
detect the remnants of def