Need help with

Express in quantiers:

The sequence {A n}n is element of natural numbers, is strictly decreasing

Give the negation of as well.

I am thinking for all N ,there exists x1 < x2, then f(x1) > f(x2) , kinda of lost...

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- Jul 30th 2011, 06:45 AMlukeheseldenquantifiers
Need help with

Express in quantiers:

The sequence {A n}n is element of natural numbers, is strictly decreasing

Give the negation of as well.

I am thinking for all N ,there exists x1 < x2, then f(x1) > f(x2) , kinda of lost... - Jul 30th 2011, 06:58 AMPlatoRe: quantifiers
There are of course several different ways one might do this.

Here is one. $\displaystyle \left( {\forall m \in \mathbb{N}} \right)\left( {\forall n \in \mathbb{N}} \right)\left( {m > n \to x_m < x_n } \right)$

The negation is, $\displaystyle \left( {\exists j \in \mathbb{N}} \right)\left( {\exists k \in \mathbb{N}} \right)\left[ {j > k \wedge x_j \geqslant x_k } \right]$ - Aug 1st 2011, 06:22 AMpeceRe: quantifiers
You mixed up the inequalities : the sequence is strictly decreasing ; what you wrote is for a strictly increasing sequence.

I assume it's a typo, but i point it out for the original poster not to confuse everything. - Aug 1st 2011, 06:34 AMPlatoRe: quantifiers
- Aug 2nd 2011, 02:10 AMlukeheseldenRe: quantifiers
thanks guys