Pointwise convergence means at every point the sequence of functions has its own speed of convergence (that can be very fast at some points and very very very very slow at others). …

Feb 17, 2025 · I think it is common to define divergence simply as non-convergence. But authors are free to define divergence to excluded bounded sequences (oscillatory sequences and …

but I have no idea on an intuitive level how this defines convergence on a topological space. It seems to me by definition of convergence, you look at every open neighborhood of the …

I understand that when a series diverges, y doesn't approach 0 when x approaches infinity, and converging series do. But what does this say? I just want to understand some applications. …

The convergence is a property of the "tail". The math is just saying (in technical language) what you intuitively know: that by going far enough out into the tail of the sequence, you can …

Aug 7, 2017 · But I find it to be confusing, as from the above definition of convergence, $1/n$ turns out to be a Cauchy sequence. But wikipedia seems to be providing a different definition …

Oct 30, 2013 · My task is to write a precise mathematical statement that "the sequence $(a_n)$ does not converge to a number $\\mathscr l$" So, I have my definition of a convergent …

In proving convergence of sequences using this definition: A sequence $ (𝑎_𝑛 )$ converges to $𝑐$ if for every $\epsilon>0$, there exists an index $𝑁$ so that, for all $𝑘≥𝑁$,

Exact definition of convergence Ask Question Asked 13 years, 11 months ago Modified 13 years, 11 months ago

Here is a very intuitive definition of convergence almost anywhere from ProofWiki: Sequence of function $(f_n)_{n \\in \\mathbb N}$ is said to converge almost everywhere on $ D$ to $ f$ if …