Infinite Series - decreasing/increasing

[seroth]

What exactly is the difference between "increasing/decreasing" and "strictly increasing/decreasing" ? is it similar to conditional and absolute convergence?

 

[sutupidmath]

$$(a_n)$$ is said to be increasing if for every $$n\in N$$ we have

$$a_n_+_1\geq a_n$$, the same if $$(a_n)$$ is decreasing then:

$$a_n_+_1\leq a_n$$,

If $$(a_n)$$ is strictly increasing than $$\forall n\in N$$

$$a_n_+_1> a_n$$. The same for decreasing.

 

[seroth]

that v symbol means "for all n " correct?

 

[Diffy]

Yup, and along the same lines: $$\exists$$ means "there exists at least one".

 

[seroth]

curved E ish symbol= all real numers?

edit

so what it means that "increasing" or "decreasing" has a point where a(n) is equal to a(n+1)? but strictly inc/dec means that no matter what value 'n' is, a(n) will always be > or < a(n+1) correct?

 

[Pere Callahan]

Increasing means for all n $a(n)\leq a(n+1)$. There might be some n's such that a(n)=a(n+1), but not necessarily.

Strictly increasing means for all n a(n)<a(n+1), you can never have equality.

 

[seroth]

thank you very much, i just needed clarification on that part of the equality