teaching:topics:number:making
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
teaching:topics:number:making [2020/09/15 14:39] simon |
teaching:topics:number:making [2022/02/16 23:23] (current) simon |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | ======making new numbers====== | + | <WRAP right>[[teaching:topics:number:axioms#there are important non-numbers]]</WRAP> |
| + | ===making new numbers=== | ||
| //Sometimes you can. Sometimes you cannot.// | //Sometimes you can. Sometimes you cannot.// | ||
| While exploring and developing our idea of [[teaching:topics:number:axioms:#what is a number|number]] we have invented new numbers that allow us to | While exploring and developing our idea of [[teaching:topics:number:axioms:#what is a number|number]] we have invented new numbers that allow us to | ||
| give answers to questions that we previously could not answer with a number. | give answers to questions that we previously could not answer with a number. | ||
| + | == == | ||
| Maybe you are a farmer (thousands of years ago) and you want to divide your field into three equal parts, you measure distance | Maybe you are a farmer (thousands of years ago) and you want to divide your field into three equal parts, you measure distance | ||
| by 'chains' in your part of the world. There is actually a chain kept at the surveyor's house which is | by 'chains' in your part of the world. There is actually a chain kept at the surveyor's house which is | ||
| Line 31: | Line 32: | ||
| We could find ways to do these with fractions, with negative numbers, with real numbers, even | We could find ways to do these with fractions, with negative numbers, with real numbers, even | ||
| - | with complex numbers (after we invented \(\ \rm i\ \) as the solution to `\ x^2+1=0` ). But we cannot achieve a good working definition of `infty` that lets us use it in our number algebra. | + | with Complex Numbers (after we invented \(\ \rm i\ \) as the solution to `\ x^2+1=0` ). But we cannot achieve a good working definition of `infty` that lets us use it in our number algebra. |
| [[teaching:topics:calculus:limits#Infinitessimals]] are a related problem. | [[teaching:topics:calculus:limits#Infinitessimals]] are a related problem. | ||
| Consider the [[teaching:topics:calculus:sequences#paradox|wolf and the sprinter]], a challenge has kept us wondering for millenia. | Consider the [[teaching:topics:calculus:sequences#paradox|wolf and the sprinter]], a challenge has kept us wondering for millenia. | ||
teaching/topics/number/making.1600144797.txt.gz · Last modified: 2020/09/15 14:39 by simon
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 3.0 Unported
