Ciro Santilli @cirosantilli 37

Like isomorphism, but does not have to be one-to-one: multiple different inputs can have the same output.

The image is as for any function smaller or equal in size as the domain of course.

This brings us to the key intuition about group homomorphisms: they are a way to split out a larger group into smaller groups that retains a subset of the original structure.

As shown by the fundamental theorem on homomorphisms, each group homomorphism is fully characterized by a normal subgroup of the domain.

China related: cirosantilli.com/china-dictatorship/dictatorship

While Ciro Santilli is a big fan of having "one global country" (and language), which is somewhat approximated by globalization, he has come to believe that there is one serious downside to globalization as it stands in 2020: it allows companies to pressure governments to reduce taxes, and thus reduces the power of government, which in turn increases social inequality. This idea is very well highlighted in Can't get you out of my head by Adam Curtis (2021).

The only solution seems to be for governments to get together, and make deals to have fair taxation across each other. Which might never happen.

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

As shown in Video "Simple Groups - Abstract Algebra by Socratica (2018)", this can be split up into two steps:This split is sometimes called the "Jordan-Hölder program" in reference to the authors of the jordan-Holder Theorem.

Good lists to start playing with:

History: math.stackexchange.com/questions/1587387/historical-notes-on-the-jordan-h%C3%B6lder-program

It is generally believed that no such classification is possible in general beyond the simple groups.

Bibliography:

Ciro Santilli has already watched all the best films in history, and as a result any of those new movies that is full of clichés and has no innovative aspect at all (99.99999% of all modern movies) makes Ciro want to puke and to start Googling TV Tropes to classify as many clichés as possible.

Good movies are those that teach you mechanisms of the real world. Willing suspension of disbelief must be maintained at all costs.

Or of what could happen a world where a single sci-fi element is added and explored to its limits.

Love is not an interesting aspect of the world. You solve your love life at university, Tinder or Tango.

The actually interesting aspects of the world are:

Movies with a lot of action scenes, with exception of some war movies, are shit.

The Sliding scale of idealism vs. cynicism must be close to Cynicism max at all times. Movies with pure good and pure bad are shit.

Knowing spoilers has no effect in the film's enjoyment. The interest of storyline concepts is all that matters, visuals and acting are useless.

In a multi-language film, when two foreign characters speak English to each other when they obviously would have spoken their native language, that is a crime. Original language + subtitles is a must!

TEM: sample has to be very thin, you get a 2D image. Higher resolution possible.

SEM: sample does not need to be ultra thin, you get a 3D image. Lower resolution possible.