Introduction

Notes

Math

Epistemology

Search

Andrius Kulikauskas

  • m a t h 4 w i s d o m - g m a i l
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

用中文

  • 读物 书 影片 维基百科

Introduction E9F5FC

Questions FFFFC0

Software


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.
Edit - Upload - History - Print - Recent changes
Search:
This page was last changed on February 23, 2022, at 02:56 PM