f-0-R-a-N-R-a-n-1-f-a-n-a-n-f-x-f-y-x-y-0-does-a-n-a-m-n-m-0-

Question Number 1963 by 123456 last updated on 26/Oct/15

f : [0, + \infty) \to R, a : N \to R

a_{n + 1} = f (a_{n}) - a_{n}

f (x) ⩾ f (y), \forall x ⩾ y ⩾ 0

does

a_{n} ⩾ a_{m}, \forall n ⩾ m ⩾ 0 ?

Answered by prakash jain last updated on 26/Oct/15

Counter example

a_{0} = 1

f (1) = 0 \Rightarrow f (a_{0}) = 0

a_{1} = 0 - 1 = - 1

a_{1} < a_{0}

Commented by Rasheed Soomro last updated on 27/Oct/15

a_{0} = 1 A s s u m e d ?

f (1) = 0 H o w ? I s i t a l s o a s s u m p t i o n ?

Q u e s t i o n f o r s a k e o f u n d e r s t a n d i n g / K n o w l e d g e .

N o t o b j e c t i o n .

Commented by prakash jain last updated on 27/Oct/15

Values assumed which satisfy the given

conditions in question to create a counter

example .

We can also use a_{1} and a_{2} and use differnt

values to create a counter example as long as

f (a_{1}) - a_{1} < a_{1}

f (a_{1}) < 2 a_{1}

Commented by Rasheed Soomro last updated on 27/Oct/15

{THANK}^{S}!