<<Mr. Harper quotes from Hardy's "A Course of Pure Mathematics" 10th ed
Cambridge 1952 , p186 , first the definition of continuity and then, from
p.189
"The function which is equal to 1 when x is rational and to 0 when x is
irrational (Ch. II, Ex. XVI. 10) is discontinuous for all values of x. So too
is any function which is defined only for rational or for irrational values of
x."
[In order to verify this quotation, I have taken the pains to waddle to the
mathematics library here which does not have the 10th but the 4th edition of
Hardy's book. Mr. Harper's quotation there occurs verbally as the second in
the list of "Examples" on p.176.]>>
Since I am lazier than professor Felscher (or perhaps, after the American
Thanksgiving, not well able to waddle), I am still hoping to be told in the
course of this increasingly enlightening exchange (for which, much thanks)
when the *first* edition of Hardy's book was published. Obviously it was a
key text for more than a generation, and I wonder if there is a written
account of it from a historian of mathematics somewhere.
Happy Thanksgiving from Brooklyn
-Bill Everdell