Proving that left limit for a function exists

[Halen]

the question states:

suppose that f:(0,1)--->R is a (strictly) increasing function.
suppose also that there is a constant MeR such that f(x)<M for xe(0,1). prove that the left limit of f exists?

how would you use the information about the function being strictly increasing?

Thank you!

 

[gb7nash]

the question states:

suppose that f:(0,1)--->R is a (strictly) increasing function.
suppose also that there is a constant MeR such that f(x)<M for xe(0,1). prove that the left limit of f exists?

how would you use the information about the function being strictly increasing?

Thank you!

When you say the left limit of f, do you mean:

$$\lim_{x\to 1^{-}}f(x)$$

?

 

[Halen]

oh yes.. sorry!