Thread: 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

Originally Posted by pankaj

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

Monotonic function - Wikipedia, the free encyclopedia

Originally Posted by pankaj

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

f is an increasing function if and only if a> b implies .

f is a strictly increasing function if and only if a> b implies f(a)> f(b.

Notice that those definitions do NOT require the function to be differentiable and the first allows the function to be constant on an interval. Indeed, a constant function is "increasing" in that sense.

Note: some textbooks use "increasing" in the sense of "strictly increasing" here and use "non-decreasing" in the sense of "increasing" here.

This is what was confusing me