Proof that f is injective?

• July 20th 2010, 04:43 PM
kensington
Proof that f is injective?
How would i go about solving this problem?

Attachment 18261

• July 20th 2010, 07:29 PM
tonio
Quote:

Originally Posted by kensington
How would i go about solving this problem?

Attachment 18261

Either I'm missing something or this is immediate: $x\neq y\Longrightarrow |f(x)-f(y)|=c|x-y|^\alpha > 0$ , and we're done...

Tonio
• July 20th 2010, 11:53 PM
HallsofIvy
Yes, you can start with f(x)= f(y) which, using Tonio's point, immediately gives x= y.