A generalized definition of derivative that works on manifolds.

TODO: how does it maintain a single value even across different coordinate charts?

Being a complex holomorphic function is an extremely strong condition.

The existence of the first derivative implies the existence of all derivatives.

Another extremely strong consequence is the identity theorem.

"Holos" means "entire" in Greek, so maybe this is a reference to the fact that due to the identity theorem, knowing the function on a small open ball implies knowing the function everywhere.

Once upon a time in the 2010's, Ciro Santilli went to an artsy theatre venue in the suburbia of Paris, dragged by his wife then girlfriend of course.

In the venue, there was a politician, who was doing his best to show how much they supported the arts, and there were of course the artists, involved in the play.

The politician would see a political power score on top of every person's head, and would spend an amount of time talking to each person exactly proportional to that score. This meant basically one sentence to us. The words themselves didn't really matter of course, only the time spent, they just have to produce nice sounds.

One of the artists however, and he seemed quite important in the production, for some reason spent a huge amount of time speaking to us. The score the artist saw on our heads was of love, or how interested we were in the art.

A good definition is that the sparse matrix has non-zero entries proportional the number of rows. Therefore this is Big O notation less than something that has $N^2$ non zero entries. Of course, this only makes sense when generalizing to larger and larger matrices, otherwise we could take the constant of proportionality very high for one specific matrix.

Of course, this only makes sense when generalizing to larger and larger matrices, otherwise we could take the constant of proportionality very high for one specific matrix.

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.

Grouping their mouse brain projcts here.

math.stackexchange.com/questions/700235/is-there-an-easy-proof-for-the-classification-of-6-transitive-finite-groups says there aren't any non-boring ones.

Per-table dumps created with mysqldump and listed at: dumps.wikimedia.org/. Most notably, for the English Wikipedia: dumps.wikimedia.org/enwiki/latest/

A few of the files are not actual tables but derived data, notably dumps.wikimedia.org/enwiki/latest/enwiki-latest-all-titles-in-ns0.gz from Download titles of all Wikipedia articles

The tables are "documented" under: www.mediawiki.org/wiki/Manual:Database_layout, e.g. the central "page" table: www.mediawiki.org/wiki/Manual:Page_table. But in many cases it is impossible to deduce what fields are from those docs.

The first chapter of the New Testament.