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The arrow diagram used to define the function above can be very helpful in visualizing functions. We will often be working with functions with finite domains, so this kind of picture is often more useful than a traditional graph of a function.
ArrowDiagramof Functions •The definition of a function implies that the arrow diagram for a function f has the following two properties: •Every element of Ahas an arrow coming out of it •No elements of Ahas two arrows coming out of it that point to two different elements of B.
Arrow Diagrams Recall from Section 1.3 that if X and Y are finite sets, you can define a function f from X to Y by drawing an arrow diagram. You make a list of elements in X and a list of elements in Y,anddrawanarrowfromeachelementinX to the corresponding element in Y,asshowninFigure7.1.1. x1 x 2 x 3 x4 y1 y y y4 y5 XYf Figure 7.1.1
Thus an arrow diagram for a function from a finite set to a smaller finite set must have at least two arrows from the domain that point to the same element of the co-domain. In Figure 7.3.1(b), arrows from pigeons 1 and 4 both point to pigeonhole 3.
The arrow diagram used to define the function above can be very helpful in visualizing functions. We will often be working with functions with finite domains, so this kind of picture is often more useful than a traditional graph of a function.
Arrow Diagram of a Relation For relation R from A to B, draw an arrow from a to b iff aRb. < f(1;2);(1;3);(2;3)g [3] [3] 1 2 3 1 2 3 = f(1;1);(2;2);(3;3)g [3] [3] 1 2 3 1 2 3
14 maj 2024 · One way is to use an arrow diagram to represent the mappings between each element. We write the elements from the domain on one side, and the elements from the range on the other, and we draw arrows to show that an element from the domain is mapped to the range.
