Definition:Limit of a Sequence (Number Field)
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Definition
As:
- The set of rational numbers $\Q$ under the usual metric forms a metric space
- The real number line $\R$ under the usual metric forms a metric space
- The complex plane $\C$ under the usual metric forms a metric space
the definition of the limit of a sequence in a metric space holds for sequences in the standard number fields $\Q$, $\R$ and $\C$.
Now define it.
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Sources
- W.A. Sutherland: Introduction to Metric and Topological Spaces (1975): Definition $1.2.2$
- K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 4.4$
