Increasing and Strictly increasing

A function is said to be increasing on if for every where then

I read in a book that function is increasing on if on the interval (but should not become zero on any sub-interval of

This is given in standard texts

So what exactly does strictly increasing mean i.e when is a function said to be strictly increasing on the interval .

The definition of strictly increasing was given as follows:

The function is strictly increasing on if on the interval

A confusion gets created with regard to use of sign and sign

So what exactly is the definition of increasing function and what exactly is the definition of strictly increasing function