'Minimal element' diaporamas de présentation

Classical (crisp) set

Classical (crisp) set. A collection of elements or objects x ?X which can be finite , countable , or overcountable . A classical set can be described in two way: Enumerating (list) the elements ? describing the set analytically Example: stating conditions for membership --- {x|x?5}

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Proof by the Well ordering principle

Proof by the Well ordering principle. Well Ordering Principle. Every nonempty set of nonnegative integers has a least element. Well Ordering Principle. Every nonempty set of nonnegative integers has a least element. Well Ordering Principle.

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Proof by the Well ordering principle

Proof by the Well ordering principle. Well Ordering Principle. Every nonempty set of nonnegative integers has a least element. Well Ordering Principle. Every nonempty set of nonnegative integers has a least element. Well Ordering Principle.

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Data Compression

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Data Compression

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Section 4.4 Inductive Proof

Section 4.4 Inductive Proof What do we believe about nonempty subsets of N ? Since ? N , < ? is well-founded, and in fact it is linear, it follows that every nonempty subset has a least element. This little observation is the only thing we need to present the ideas of inductive proof.

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Creating Heaps

Creating Heaps. Heap is an array-based implementation of a binary tree used for implementing priority queues, supports: insert, findmin, deletemin: complexities? Using array minimizes storage (no explicit pointers), faster too --- children are located by index/position in array

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