Hey all, I've lurked on here and have found you all very useful and I have this question that is really bugging me. How would you prove something is a cauchy sequence using tits definition. Physics news on Phys.org New organic molecule design can lead to long-lasting, durable OLEDs ...
Completeness refers to a metric space where every Cauchy sequence converges, while compactness refers to a subset of a metric space that is closed and bounded. In general, a metric space can be complete without being compact, and vice versa. ...
No, the Monotone Convergence Theorem is not a necessary condition for convergence. There are other convergence tests, such as the Cauchy Convergence Criterion, that can also be used to prove convergence of a sequence. Can the Monotone Convergence Theorem be applied to sequences in o...
When we face a problem whose answer is a sequence of numbers a 0 , a 1 , a 2 , … and we want to know what the closed mathematical expression is that enables us to obtain the element a n of that sequence. Sometimes, we can do it at first sight by inspection. For example, if ...
When we face a problem whose answer is a sequence of numbers 𝑎0,𝑎1,𝑎2,… and we want to know what the closed mathematical expression is that enables us to obtain the element 𝑎𝑛 of that sequence. Sometimes, we can do it at first sight by inspection. For example, if the...