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.
You can use the comparison test. Since the convergent sequence divided by n is less that the convergent sequence, it must converge.
JUB
Every convergent sequence is Cauchy. Every Cauchy sequence in Rk is convergent, but this is not true in general, for example within S= {x:x€R, x>0} the Cauchy sequence (1/n) has no limit in s since 0 is not a member of S.
(0,1,0,1,...)
no converse is not true
If a monotone sequence An is convergent, then a limit exists for it. On the other hand, if the sequence is divergent, then a limit does not exist.
A convergent sequence is an infinite sequence whose terms move ever closer to a finite limit. For any specified allowable margin of error (the absolute difference between each term and the finite limit) a term can be found, after which all succeeding terms in the sequence remain within that margin of error.
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.
which literary term is defined as stories or events told in the sequence in which they happen
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.