How to construct a bijection between $[1,6)$ and $(-3,3)$?
I've tried to come up with a proper bijection, but haven't had any luck. Any ideas how to solve it?
Asked
Active
Viewed 39 times
1
-
1Hint: First, biject $[1,6)$ with $(0,1]$. Second (the hard part), biject $(0,1]$ with $(0,1)$. Last, biject $(0,1)$ with $(-3,3)$. – vadim123 Dec 12 '17 at 18:29
-
@vadim123 I haven't thought about it that way. Thanks for the tip, it sure made it easier. – MathBear Dec 12 '17 at 18:32
-
The very short answer is that your function cannot be continuous. – Doug M Dec 12 '17 at 18:33