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