Ciro Santilli @cirosantilli 40

OMG, the second half of the game where the world becomes quite open and all backstories are revealed, is one of the best gaming moments ever.

The financial industry does not serve society nowhere near its magnitude (London of course being the epitome of that). It serves only itself. It just grows without bound.

In Chinese lit. just "Four Great Masterpieces".

Examples:

Used to solve partial differential equation.

TODO understand, give intuition, justification of bounds and JavaScript demo.

A convenient notation for the elements of $GF(n)$ of prime order is to use integers, e.g. for $GF(7)$ we could write:which makes it clear what is the additive inverse of each element, although sometimes a notation starting from 0 is also used:

For fields of prime order, regular modular arithmetic works as the field operation.

For non-prime order, we see that modular arithmetic does not work because the divisors have no inverse. E.g. at order 6, 2 and 3 have no inverse, e.g. for 2:we see that things wrap around perfecly, and 1 is never reached.

For non-prime prime power orders however, we can find a way, see finite field of non-prime order.

As per classification of finite fields those must be of prime power order.

Video "Finite fields made easy by Randell Heyman (2015)" at youtu.be/z9bTzjy4SCg?t=159 shows how for order $9=3\times 3$. Basically, for order $p^n$, we take:For a worked out example, see: GF(4).

Builds on top of propositional logic, adding notably existential quantification.

Once Ciro joked in a twenty questions-like game that humans are animals.

But counting humans a fish would have been a stroke of genius.

Synthesizes MIDI input. vmpk + aconnect + Advanced Linux Sound Architecture hello world: askubuntu.com/questions/34391/virtual-midi-piano-keyboard-setup/1298026#1298026

Supports only very basic effects it seems: chorus effect and reverberation. The main way to add instruments to it is via SoundFont files.

Completeness: math.stackexchange.com/questions/2192665/is-this-set-of-bessel-functions-a-basis-for-all-c10-a-functions TODO

This is the Bessel function analogue to Fourier basis is complete for $L^2$.

A set of theorems that prove under different conditions that the Fourier transform has an inverse for a given space, examples: