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


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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

	${THANK}^{S}!$
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