Ciro Santilli @cirosantilli  40

www.youtube.com/watch?v=0hfdSrK46EE How To Use A Minimoog Synthesizer by Doctor Mix (2020)

Software emulators:

See also some remarks of Ciro Santilli's thoughts on the instrument Ciro Santilli's musical education.

Something analogous to a group isomorphism, but that preserves whatever properties the given algebraic object has. E.g. for a field, we also have to preserve multiplication in addition to addition.

Other common examples include isomorphisms of vector spaces and field. But since both of those two are much simpler than groups in classification, as they are both determined by number of elements/dimension alone, see:we tend to not talk about isomorphisms so much in those contexts.

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.

Two numbers such that the greatest common divisor is 1.

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

This is a list of video games that are good to watch other people playing, even if you don't play yourself. And often they are better to watch than to play as you don't have to waste your time as much!

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.

You select a generating set of a group, and then you name every node with them, and you specify:

Not unique: different generating sets lead to different graphs, see e.g. two possible en.wikipedia.org/w/index.php?title=Cayley_graph&oldid=1028775401#Examples for the