Infinite Series - decreasing/increasing

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Main Question or Discussion Point

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

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[tex] (a_n)[/tex] is said to be increasing if for every [tex]n\in N[/tex] we have

[tex] a_n_+_1\geq a_n[/tex], the same if [tex](a_n)[/tex] is decreasing then:

[tex] a_n_+_1\leq a_n[/tex],

If [tex](a_n)[/tex] is strictly increasing than [tex]\forall n\in N[/tex]

[tex] a_n_+_1> a_n[/tex]. The same for decreasing.
 
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that v symbol means "for all n " correct?
 
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Yup, and along the same lines: [tex]\exists[/tex] means "there exists at least one".
 
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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?
 
Last edited:
Increasing means for all n [itex]a(n)\leq a(n+1)[/itex]. 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.
 
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thank you very much, i just needed clarification on that part of the equality
 

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