01:640:107 Lecture Notes - Lecture 3: Natural Number, Commutative Property, 5,6,7,8
9 Dec 2016
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Document Summary
Properties applied to create the standard (and other) addition algorithms. Consequently, we will use the commutative and associative properties (which involve positioning and grouping, respectively) implicitly when we work with natural numbers, as well as explicitly when we work with the operations on natural numbers. Specifically, for the base ten system we use the digits or symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and we know from experience that every natural number can be represented using those digits. The numbers 1 through 9 are defined to be the 1 that is the first element of the natural numbers regardless of how we represent them, and its immediate successors up to 9. The number 10 is different (as it uses two digits) and is the successor of 9. And then the place value system in base 10 proceeds as follows: the sum of two groups of ten is denoted 20 (that is, 10.
