Definition:Convergent Sequence/Real Numbers/Graphical Illustration
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Definition
The following diagram illustrates the first few terms of a convergent real sequence.
For the value of $\epsilon$ given, a suitable value of $N$ such that:
- $n > N \implies \size {x_n - l} < \epsilon$
is $6$.
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $1$: Review of some real analysis: $\S 1.2$: Real Sequences: Definition $1.2.2$
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 4$: Convergent Sequences: $\S 4.4$: Definition of Convergence