algebraic geometry and Galois theory 1

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This videos is a soft introduction to algebraic geometry and Galois theory.
We have introduced:
algebraic sets, affine schemes, schemes,
Galois groups, the main theorem of Galois, Galois--Grothendieck theorem,
Categories, simplical sets
Bibliography:
D. Coray "Notes on Geometry and arithmetics"
Yu. Manin "Scheme theory"
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Hello! In the example at @15:25 of the talk, could someone please verify which is the identity element of that particular monoid? I have the impression it must be the concatenation with the empty set, but in the previous example the set {0, 1, 2, ...} we have an explicit element namely zero, for the identity element. So I am not sure... Thanks.

constantinoskourouzides
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I just wonder if you could help me to find the solution of two fluid vortex crashing each other creating a membrane and multiple vortex rings

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