It could be divergent eg 1+1+1+1+...
Or, it could be oscillating eg 1-1+1-1+ ...
So there is no definition for a sequence that is not convergent except non-convergent.
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no converse is not true
Lexicographic preferences are not continuous because of the decreasing convergent sequence.
A sequence cannot be defined by one number. At least, not a sequence of any value.
If the sequence is non-linear, you need to establish how it is defined.
No. An 'arithmetic' sequence is defined as one with a common difference.A sequence with a common ratio is a geometricone.