A possible concise summary is:
The speaker explains what a function is in mathematics, using diagrams and examples of sets and rules of correspondence. A function is a rule that associates each element of a starting set with a single element of an arrival set. The speaker shows how to use symbols and expressions to represent functions, and how to check if a diagram is a function or not. The speaker also gives an exercise for the listeners to practice identifying functions.
Here are the key facts extracted from the text:
1. There is a set A with three elements.
2. There is a set B with four elements.
3. Set A contains the elements -10 and 2.
4. Set B contains the elements -2011 and 4.
5. There is a correspondence between sets A and B.
6. Each element from A is associated with its double in B.
7. The starting set is A, and the arrival set is B.
8. No elements are left in the starting set after association.
9. Each element of A has a unique corresponding element in B.
10. The function goes from set A to set B.
These facts are based on the instructions and descriptions provided within the text regarding sets, their elements, and the rules of correspondence between them.