CU Boulder News & Events: An Approximate Dynamic Programming Approach to Dynamic Stochastic Matching
In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical Operators B...
(If you do not want complex approximate solutions, ignore the complex approximate solutions; that still leaves two real approximate solutions.) This approximation improves "as fast as" $-1/x$ becomes negligible in your application.
The way you have written it, an approximate identity is a sequence that converges to $\Bbb1$ in a weaker sense than norm topology. In this case you have written that it converges to $\Bbb1$ in the strong operator topology.
In general, if you want to approximate an ellipse with circular arcs, you need two consecutive arcs to have the same tangent at the common endpoint, to give a smooth enough curve.
@DeanMiller: I think it helps, but it is a bit confusing as the OP uses a definition of approximate spectrum that differs from Wikipedia's but which according to the addendum of the accepted answer is equivalent. However, this is not the definition used in the main part of the answer! Moreover, they don't show the equivalence but only the implication in one direction.
From the book "Numerical Methods for Engineers", by Steven C. Chapra, they state the true error is always less than the approximate error, and therefore, it is safe ...
But WolframAlpha approximate the sum to $0.9015$ , what’s the wrong ? find a positive integer $n$ such that $S_n$ approximates the sum of the series to 4 decimal places.