L05C - Short History of Numbers 1) When Mother still dwelt...

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Short History of Numbers 1) When Mother still dwelt in the trees and counted fingers, bananas, and chil- dren, she invented the Natural Numbers { N , + , × , ≤} N def = { 1 , 2 , 3 ,... } . This enabled her to solve equations like a + x = b , a < b . 2) When she started a small business trad- ing bananas, she experienced the need to solve equations like 5 + x = 3 . This cannot be done in N , so she extended the number system by adding zero and
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negative integers, arriving at the larger number system { Z , + , × , ≤} Z def = { 0 , 1 , - 1 , 2 , - 2 ,... } . of Integers . 3) When she had a birthday party with 5 kids but bananas only for 3 birthday cakes, she experienced the need to solve equations like 5 × x = 3 . Namely, she knew that she must give ev- ery kid an equal amount x of cake lest she invite a mutiny. She found it easier to extend the number system again, to the Rational Numbers { Q , + , × , ≤} Q def = { m/n : m,n Z ,n 6 = 0 } . 2
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4) After the birthday party every piece of cloth in her hut was soiled, so she washed all. Since it rained, she decided to hang up the laudry to dry inside her hut. She needed a clothesline the length of the di-
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L05C - Short History of Numbers 1) When Mother still dwelt...

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