Another question, sorry Final Friday, senior year, this class is horrible
Let f: D-->R be uniformly continuous on D and let cED. Prove using an
epsilon-delta argument cf is uniformly continuous on D.
R = Real Numbers
Another question, sorry Final Friday, senior year, this class is horrible
Let f: D-->R be uniformly continuous on D and let cED. Prove using an
epsilon-delta argument cf is uniformly continuous on D.
R = Real Numbers
let $\displaystyle \epsilon > 0$
Since f is uniformly continuous there exisits a delta for every epsilon such that
$\displaystyle |x-y|< \delta$ $\displaystyle |f(x)-f(y)|<\frac{\epsilon}{|c|}$
Now for $\displaystyle |x-c|< \delta$
$\displaystyle |cf(x)-cf(y)|=|c||f(x)-f(y)|<|c|\cdot \frac{\epsilon}{|c|}=\epsilon$
QED