Chatting about REAL numbers

The term "real number" confuses many who are not immersed in mathematics.  For these, to whom 1, 2, 3 and the other counting numbers seem most real, the identification of the real numbers as all infinite decimals (i.e., all numbers representable by points on a number line) seems at first to go beyond intuition.  But, upon further reflection, the idea of a number as "real" iff it can represent a distance on a line to the right or left of a central origin, 0, indeed seems reasonable.

Professor Fred Richman of Florida Atlantic University takes on the questions of computability and enumerability of the real numbers in his poem, "Dialogue Between Machine and Man":

Ghosts of Departed Quantities

     Years ago in calculus class I excitedly learned that an infinite number of terms may have a finite sum.  Manipulation of infinities seems somewhat routine to me now but my early ideas of calculus enlarged me a thousand-fold.  Algebra was a language, geometry was a world-view, and calculus was a big idea.  Like any big idea, even though it had been hundreds of years in formation, it met with resistance.  In 1764 Bishop George Berkeley attacked the logical foundations of the calculus that Isaac Newton had unified.  Here, from the online mathematics magazine plus,  is a description of the attack.