teaching:topics:number:axioms
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teaching:topics:number:axioms [2021/09/25 23:00] simon [some important ideas first ...] |
teaching:topics:number:axioms [2024/03/14 13:03] (current) simon [some important ideas first ...] |
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| **=>[[axioms-formal#a more formal way to define numbers]]** | **=>[[axioms-formal#a more formal way to define numbers]]** | ||
| - | We use them along with arithmetic like `times` and `+` to help us describe and understand many properties of the world we observe around us. | + | <WRAP #rationale/>We use them along with arithmetic like `times` and `+` to help us describe and understand many properties of the world we observe around us. |
| An astonishing variety of very different quantities we measure behave like numbers and have important properties derived using arithmetic. | An astonishing variety of very different quantities we measure behave like numbers and have important properties derived using arithmetic. | ||
| In physics we measure distance, time, mass and electrical charge and from them calculate properties like position, area, volume, speed, acceleration, force, pressure, temperature, density and energy to build a model of the way physical things interact. | In physics we measure distance, time, mass and electrical charge and from them calculate properties like position, area, volume, speed, acceleration, force, pressure, temperature, density and energy to build a model of the way physical things interact. | ||
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| <wrap #Order_of_operations />//Order of operations// in arithmetic:\\ | <wrap #Order_of_operations />//Order of operations// in arithmetic:\\ | ||
| - | do the brackets first; then any powers; then multiply and divide; then finally plus and minus. | + | do the brackets first;\\ <wrap indent/>then any powers;\\ <wrap indent/><wrap indent/>then multiply and divide;\\ <wrap indent/><wrap indent/><wrap indent/>then finally plus and minus. |
| <wrap #distributive />**distributive** tells how `+` and `times` work together, `quad 2times(3+4)=(2times3)+(2times4)=14`. This looks much neater (and is easier to read and understand) in our algebra notation where we do not use the `times` symbol... | <wrap #distributive />**distributive** tells how `+` and `times` work together, `quad 2times(3+4)=(2times3)+(2times4)=14`. This looks much neater (and is easier to read and understand) in our algebra notation where we do not use the `times` symbol... | ||
teaching/topics/number/axioms.1632574803.txt.gz ยท Last modified: 2021/09/25 23:00 by simon
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