/sci/ - Science & Math

>>11194198
I think the first only over the dividing ones (to some power), while the second (for k>1) takes into account how to further divide that divisor.
quote
> More generally, one defines (...) where dk(n) counts the number of ways that n can be written as a product of k numbers

>>11194233
I'd be interested in that too - although I'd think it's hard to find an audience. I'd do podcasts if people were interested. Needs people who're reed a lot (or work really a lot) and willing to rant about that periodically - do you know any such folks?

>>11194198
the second sums over all naturals smaller than the argument, the first only over the dividing ones

>>11194233
I'd be interested in that too - although I'd think it's hard to find an audience. I'd do podcasts if people were interested. Needs people who're reed a lot (or work really a lot) and willing to rant about that periodically - do you know any such folks?

>>10981512
I can stomach it to an extent, but given my field is specific enough, I'd like to see an algebraic number field approach, seeing where the new elements of the field extension end up in some explicit matrix calculations - if that's rich enough and studied

>>10946913
Just md files with sections seperated by # or ## etc. and then bullet points or plain text.
https://gist.github.com/Nikolaj-K/951d44b393a92acc51f915fcb0e31cc2
When I feel like writing a plain text that I'll still understand in a few years, I translate it to e.g.
https://axiomsofchoice.org/ito_integral

>>10946895
People will disagree with this and then /sci/ gives each other shit about everything and in an unnecessary agressive way. So let me take some hits...

What's certainly true is that if you stand in a lab as a chemistry PhD 10 hours a day looking through a device and writing down how some liquits behave when mixed toghether - you're not doing math.
"Doing math" at an uni and for pure math will likely involve doing something that's trying to be innovative (and if not creatively, then at the very least in a way that notes down properties of things).
"Hard math" in engineering and applied physics might involve coming up with new tricks, but even solving complicated fluid dynamics numericalls will tend to involve the sort of conceptural setup that was establishe in math in the 1800'th. So Engineering work in differential equations will be barely interesting for mathematicans and mathematicans work on the same subject is of little help to the practical side.
Wwith high energy physics research (where physicists working in the field don't necessarily expect that there will be an experiment in their lifetime validating the ideas), you can say it's mostly a matter of interest in the field - while both do math. However, the half-life of math theories (hip trends) tends to be much longer than in physics departments. Let's say physics trends in academia can be years or a decade (say this and that path integral method in thi and that vaguely defined uncountably infinite dimensional vector space with applications for this and that sort of polymeres) while a lot of math theories survives for many decades (centuries in some cases, say combinatorics).

How does [math] \aleph_\omega [/math] relate to [math] V_\omega [/math]?

And how do they relate to the cardinality of higher order function spaces such as [math] ( { \mathbb R } \to { \mathbb R } ) \to { \mathbb R } [/math], given that already. [math] | { \mathbb R } \to \{ 0, 1 \} | > | { \mathbb R } | [/math]

inspired by the math I do atm., usually