Does it converge ?

Calculus Level 3

Does the sequence { 1 n : n ∈ N } \left \{ \dfrac{1}{n}: n \in \mathbb{N} \right \} converge?

definitely yes definitely no it depends

Hobart Pao by Hobart Pao , 23, USA

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1 solution

Hobart Pao
Feb 21, 2018

It depends on the metric space the sequence is in. If the metric space for example is all positive rational numbers and uses the conventional distance formula as a metric, the sequence does not converge because 0 0 isn't positive.

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