b) prove that if there is f which gets a unique value for each x and continues in R ,
$\displaystyle lim_{x->\infty}f(x)=\infty$

then f monotonickly increasing in R.

i tried like this:
monotonickly increasing is when for every x>y then f(x)>f(y).

suppose there is 't' in R
we can choose M>y
by the limit definition for x>M f(x)>N=|t|+1>t
if we say that t=f(y)
the we get the f(x)>f(y) which is the definition we need to proove
is it correct