Only briefly continuous (Posted on 2005-12-15)

	Submitted by Tristan
Rating: 3.5000 (2 votes)
Solution:	(Hide)
f(x) = { x2 if x is rational { 0 if x is irrational This function is related to the Dirichlet function, which is equal to 0 for rationals and 1 for irrationals. The Dirichlet function is never continuous, but here, f(x) is continuous at 0 and only 0. The particular function I chose is also differentiable only at the single point x=0.

	Subject	Author	Date
	Puzzle Answer	K Sengupta	2023-11-25 06:51:25
	re(4): Another thought	goFish	2005-12-17 10:37:54
	re(3): Another thought	Larry	2005-12-17 09:41:08
	re(2): Another thought	goFish	2005-12-16 03:13:40
	Function named	MindRod	2005-12-15 23:32:10
	re: Another thought	MindRod	2005-12-15 23:28:16
	Another thought	Larry	2005-12-15 20:46:51
	re: Non-piecewise	Richard	2005-12-15 14:57:49
	Non-piecewise	Jer	2005-12-15 14:34:42
	See Also	Richard	2005-12-15 12:45:27
	Another solution	Federico Kereki	2005-12-15 09:44:28
	A solution	goFish	2005-12-15 08:19:35