#583. What is zero? What is infinity? Where they come from?

Mathematics, level: Senior
Posted Sat Aug 22 14:12:22 PDT 1998 by Hossein Arsham (harsham@ubmail.ubalt.edu).
The Zero Saga and Other stories
University of Baltimore, Baltimore
Materials Required: College Mathematics
Activity Time: 2-3
Concepts Taught: A critical panoramic view of basic mathematical concepts

Culturally, our discomfort with the notion of zero is reflected in such humor as 2 plus 0 still
equals 2, even for large values, and popular retorts of similar tone. A like uneasiness occurs
in confronting infinity, whose proper use first rests on a careful definition of what is finite. Are
we mortals hesitant to admit to our finite nature? Such lighthearted commentary reflects an
underlying awkwardness in the manipulation of mathematical expressions where the notions
of zero and infinity present themselves. It is not simply a problem of ignorance by young
novitiates who have often been mangled. The same errors are commonly committed by
seasoned practitioners. Nay, even educators! These errors can frequently be found as well in
prestigious texts published by mainstream publishers.