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

?

how i tried

by the limit definition for x>M f(x)>N

so if i choose y and y+1 bigger then x

then f(y)>N and f(y+1)>N

how to show that f(y+1)>f(y)

?