- #1

daniel_i_l

Gold Member

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## Main Question or Discussion Point

Lets say we have a sequence of reals. Is it always possible to change the order to that for all n [tex]a_{n+1} >= a_n[/tex]?

Or in other words,

Does there always exist a bijective function:

f:Z->Z (where Z is the set of positive natural numbers) so that for all n

[tex]a_{f(n+1)} >= a_{f(n)}[/tex]?

Or in other words,

Does there always exist a bijective function:

f:Z->Z (where Z is the set of positive natural numbers) so that for all n

[tex]a_{f(n+1)} >= a_{f(n)}[/tex]?