L03_blanks - Day 03 Visual Models of Number Systems 2...

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1 Day 03 Visual Models of Number Systems 2 Today’s Travel Plans What did we talk about yesterday? A Visual Model for the Whole Numbers and… …Operations A Visual Model for the Integers and… • eOpErations
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2 3 What did we talk about yesterday? We saw a really abstract way of defining the whole numbers in terms of sets. How did we do that exactly? 4 What did we talk about yesterday? How did we define the operation of… “+” “-” “ ∙ “ ÷
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3 5 A Visual Model of the Whole Numbers So from our definition yesterday we know that 0 = { } Visually, Let 0 be represented by empty space. From yesterday, 1 = {0}. What is the bottom line though? Is this set the only representation of 1? What does a set need to have in order to be a representation of the number 1? 6 A Visual Model of the Whole Numbers We can let a single block represent the value 1. Therefore, two blocks represents 2… … and three blocks represent 3… … and so on and so forth
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4 7 A VM for W#’s: Operations - Addition How do we model addition in this context? a + b is modeled as the merging of two sets of blocks, one representing a and the other representing b, into a single set of blocks. The number of blocks in the merged sets is the sum “a + b” Examples What are we really doing when grouping the two sets of blocks into one set, we’re taking a Union. 8 A VM for W#’s: Operations – Addition Prop. What properties does Addition have? If you have two sets of blocks does it matter what order they are
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This note was uploaded on 07/23/2011 for the course MGF 1107 taught by Professor Staff during the Fall '08 term at University of Florida.

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L03_blanks - Day 03 Visual Models of Number Systems 2...

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