On Nov 18, 2:03pm, Walter Felscher wrote:
> Subject: [HM] An odd (mathematical) remark by GHH
>
> Professor J.F.Harper in his contribution "History of def. of continuity",
> from November 17th, has drawn our attention to an odd remark by the great
> G.H.Hardy.
>
> 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. ]
>
> This "So too .." sentence of Hardy's is very odd indeed, because (i)
> while it is not quite clear what the "so" refers to and (ii) it suggests
> to be read to imply that the restriction of Dirichlet's function to
> rational arguments only, or to irrational arguments only, be discontinuous!
>
> We can be safe to assume that GHH did not want draw to such asinine
> conclusion, but what then did he mean by the "So too .. " sentence ? Has
> anyone ever commented on this ?
>
> W.F.
>
>-- End of excerpt from Walter Felscher