function continuous at only one point
It is not difficult to see that is continuous at . Indeed, if is a sequence converging to . Then
On the other hand, we can also construct a sequence of rational numbers converging to . For example, if is irrational, this follows as the rational numbers are dense in , and if is rational, we can set . For this sequence we have
In conclusion is not continuous at .
- 1 Homepage of Thomas Vogel, http://www.math.tamu.edu/ tom.vogel/gallery/node3.htmlA function which is continuous at only one point.
|Title||function continuous at only one point|
|Date of creation||2013-03-22 14:56:19|
|Last modified on||2013-03-22 14:56:19|
|Owner||Andrea Ambrosio (7332)|
|Last modified by||Andrea Ambrosio (7332)|
|Author||Andrea Ambrosio (7332)|