Use the following steps to prove that the sequence xn has no convergent subsequences if and only if ix n i + 00 as n + 00. a) suppose that the sequence xn has no convergent subsequences. let m > o. prove that there exist at most finitely many values of n such that xn e [-m, m]. explain why this implies ixn i + 00 as n + 00. b) suppose ixn i + 00 as n + 00. show that xn has no convergent subsequence. (hint: exercise 1.61 may .)

Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has verticesrecall that for counterclockwise rotation about the origin, when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will becomenext, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain,therefore the correct answer is c

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