L12_filled - Day 14 Having Direction. In Life. 2 Lets...

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1 Day 14 Having Direction. .. In Life. 2 Let’s Review Some stuff from yesterday… Last time we talked about Lists Modeled By Ordered Pairs . And Relations and Function . What are their definitions? Relation : A set of ordered pairs. Function : A relation for which the first component occurs only once. A question for which multiple answers do not occur. An action applied to an object An Algorithm applied to a problem.
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2 3 Relation and Function Types Relation Surjective Function Injective Function Bijective Function 4 Relation and Function Types II Let “Q” represent the question “What does the left side element ____ link to on the right?” In this context Q(1) = a means a is the answer to “What does the left side element a link to on the right?” So in this example: , , and The ordered pairs are A relation only since applying Q to 1 makes two answers. Alternative there are two ordered pairs with component 1.
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3 5 Relation and Function Types III Ordered Pairs: Question Version: Domain: Co-domain: Range: Ordered Pairs: Question Version: Domain: Co-domain: Range: Ordered Pairs: Question Version: Domain: Co-domain: Range: Bijective: Every Co-domain element has exactly one link. Injective Only: If a Co-domain element has a link, it has only one. Surjective Only: Every Co-domain element has at least one link, may more. 6 Function in “1 st “ or “2 nd Is it a function …in the 1 st Component (from left to right) …in the 2 nd Component (from Right to Left) …in both components or, …Neither (Just a Relation) Neither 1 st Component 2 nd Component Both Components
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4 7 Meet Bob This is Bob. Bob’s going to help us learn about some of the classical and modern notions of geometry. That sure is swell of Bob. We’re going to terrorize Bob! Bob’s about to have a Bad day… 8 Bob on a Tight Rope This is Bob on a Tight Rope… Suspended above a lake filled with some very hungry alligators. Bob can only go Left or Right (but very carefully) Bob can’t go down … He’ll be gator bait. Bob can’t go up (jump) as he’ll probably fall into the waters of certain doom.
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5 9 Bob on a Tight Rope – Bird’s Eye View This is the bird’s eye view. Assuming the usual
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L12_filled - Day 14 Having Direction. In Life. 2 Lets...

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