- #1
swuster
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Homework Statement
If {cn} is a convergent sequence of real numbers, does there necessarily exist R> 0 such that |cn|≤ R for every n ∈ N? Equivalently, is {cn : n ∈ N} a bounded set of real numbers? Explain why or why not.
Homework Equations
n/a
The Attempt at a Solution
I would think this is patently obvious given the definition of convergence but I don't really know how to put the proof in words and numbers.
cn approaches some value c for large n but it can do so in a number of ways so how can i prove that there is always some R that is larger or equal to all elements cn?
Thanks for the help!