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See: Math concepts, Variables
Understand the purpose of abstraction and how mathematical concepts grow in abstraction.
Apibendrinimas
- Protas apibendrina. Kaip nagrinėti apibendrinimą? Suvokti neurologiškai (arba tinklais). Jeigu keli pavyzdžiai (ar netgi vienas) turi tam tikras bendras savybes, tada tas apibendrintas savybes gali naujai priskirti naujoms jų apibudintoms sąvokoms.
- Apibendrinimas yra "objekto" kūrimas.
Symmetric functions of the eigenvalues of a matrix. An example where substitution makes explicit more information.
Consider how mathematics grow through abstraction. Consider
- The classification of the adjoint functors. In particular, consider how the power set {$2^X$} gets replaced by sheaves, when we are building an adjoint string based on a function {$f$}. Or consider how the tensor product becomes more sophisticated when the modules are not from the same ring. And thus how abelian groups (with zero) become relevant.
- Compare with the kinds of variables as a source of abstraction.
- In what sense do abstraction and concrete examples have an adjoint relationship?
- Abstract = theory = questions. Concrete examples = answers. Theory drifts from examples.