-1
votes
3answers
71 views

Infinity and Hilbert's hotel paradox

I did some infinite series calculations while studying Fourier analysis and the concept of infinity really bugs me. I haven't read or heard not one sensible explanation yet (for me), what infinity ...
0
votes
0answers
15 views

infinite dimensional Cramer-Wold theorem

The Cramer-Wold theorem states that if every fixed linear combination of $d$ random variables converges to a normal distribution, then the $d$ variables jointly converges to a multivariate normal ...
0
votes
1answer
52 views

Comparing Improper Integrals Involving Infinity

From my current understanding: $K>J$ and $L>K$ , therefore $L>K>J$. How can I compare the first integral $I$ ?
0
votes
1answer
93 views

Identifying an Error in Determining the Convergency of an Infinite Series

Given the infinite series of $(-1)^n/(nln(n))$ for $n = 2,3,4,\ldots$ to infinity, is the series conditionally convergent, absoultely convergent, or divergent? I took two approaches to solve this ...
2
votes
1answer
623 views

speed of convergence to infinity

Lets take for example $\lim_{x\rightarrow\infty} \log(x)$, from a mathematical point of view this is $+\infty$, but from a logical point of view it's clear that $x$ converges to $+\infty$ much more ...