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). …

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. …

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 …

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 …

Nov 27, 2011 · Exact definition of convergence Ask Question Asked 14 years ago Modified 14 years ago

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 …

Apr 14, 2014 · The formal definition is that the sequence of partial sums converges. This is usually stated in calculus but often the students don't really understand the concept of …

Oct 28, 2014 · I understand the meaning of convergence and divergence but I am a little bit unsure about using this definition to prove the statements. Specifically, I am wondering what ε …

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 …

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 $𝑘≥𝑁$,