Which are "real" numbers?

The adjective "real" in the term "real number" causes confusion for many whose mathematics is casual rather than intense.  I like the mathematical definition of a number as real iff it corresponds to a point on the number line -- for this gives the abstract number a geometric counterpart (an attachment to reality) -- but there are others for whom the reality of a number depends on its emotional connections, perhaps used in ways that poet Ginger Andrews uses numbers in the following poem.