4/15/2023 0 Comments Keilser infinitesimals test![]() ![]() The visual idea was sparked by Cauchy's thinking about infinitesimals. David Tall's page on Cognitive ideas in Calculus Textbook is aside, this is aside.Ī suggestion or a rectification is warmly welcome. This is not the same as in the textbook but rather a cognitive extension. This visual proposal is only an aid for thinking, it doesn't go into interference with the textbook. In this approach, if you visualize both $\epsilon$ and $2\epsilon$ moving towards zero, their difference $\epsilon$ will also be there. (Quoting Keisler) $^$ although they will still fall into the umbrella classification of being 'An Infinite' and the same goes alike for being an 'An Infinitesimal'. My use of the word 'cognitive' would comfortably be translated as 'intuition'. if the rather below informal writing, related to physical ideas of time and motion, bothers you, please pass it as a teenager's imagination. After glancing over (just in getting a general idea like from wiki, elementary constructions) their construction in terms of equivalence classes of sequences with limit 0, I think that intuition does find its way in some form into the formulation. Whatever I wrote was on the basis of my vague ideas. All that I can say is that when I asked this question, It was the first time I had started to learn calculus and was very enthusiastic in trying to develop my own intuition and mental picture regarding infinitesimals. Edit - I wanted to acknowledge the rather repeated and possibly awkward use of the word 'Cognitive'. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |