sequences and series

quarto/limits/limits_extensions.qmd

@@ -461,16 +461,6 @@ $$
 That ${n \choose k} \leq n^k$ can be viewed as the left side counts the number of combinations of $k$ choices from $n$ distinct items, which is less than the number of permutations of $k$ choices, which is less than the number of choices of $k$ items from $n$ distinct ones without replacement – what $n^k$ counts.
 
 
-### Some limit theorems for sequences
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-The limit discussion first defined limits of scalar univariate functions at a point $c$ and then added generalizations. The pedagogical approach can be reversed by starting the discussion with limits of sequences and then generalizing from there. This approach relies on a few theorems to be gathered along the way that are mentioned here for the curious reader:
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-
-  * Convergent sequences are bounded.
-  * All *bounded* monotone sequences converge.
-  * Every bounded sequence has a convergent subsequence. (Bolzano-Weierstrass)
-  * The limit of $f$ at $c$ exists and equals $L$ if and only if for *every* sequence $x_n$ in the domain of $f$ converging to $c$ the sequence $s_n = f(x_n)$ converges to $L$.
 
 
 ## Summary