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Discrete Math - Week 5

by: Aaron Maynard

Discrete Math - Week 5 CS 2305

Marketplace > ComputerScienence > CS 2305 > Discrete Math Week 5
Aaron Maynard
GPA 3.5

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These note cover in depth the idea of set theory. We go over different types of sets and some examples of theoretical theorems.
Discrete Math for Computing I
Timothy Farage
Class Notes
Discrete math, Math, Computer Science, ECS
25 ?




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This 3 page Class Notes was uploaded by Aaron Maynard on Wednesday February 17, 2016. The Class Notes belongs to CS 2305 at a university taught by Timothy Farage in Spring 2016. Since its upload, it has received 37 views.

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Date Created: 02/17/16
Discreet Math for Computing Aaron Maynard Timothy Farage February 15 2016 Preface Tetration Function – This is a function where the f(x) is a variable exponent of itself, and itself, and itself… you get the idea? f(x) = y = xx^(x… forever) To solve this issue, we can utilize the natural log functions! y = xy ln(y) = yln(x) Highest convergence is “e”. [ln(y)]/y = ln(x) y(1/y= x Quick notice from professor: The test WILL be closed book, closed notes. It will consist of mostly negation, simplification, and some true / false questions. Set Theory There are four main sets within set theory to take note of:  Set of real numbers  Set of positive numbers  Set of integers  Rational vs Irrational In order of list above – Ƶ = {… -3, -2, -1, 0, 1, 2, 3…} + Ƶ = {1, 2, 3, 4, 5, 6, 7…} [NOTE] “0” is not included in this set because it is not considered a positive number. N = {0, 1, 2, 3, 4, 5, 6…} [NOTE] “0” is included in this set because it is an integer, in this class we will only be referring to integers x >= 0. R = {Real Numbers} Discreet Math for Computing Aaron Maynard th Timothy Farage February 15 2016 Naïve Set Theory Definition: “Informal” – A set, a collection of unique, well defined objects. Undefined terms are those to be considered to be a point, line, or set. We say that a set B is a subset of a set C, B c C, B c C If ∀x[(x ε B) -> (x ε C)] C B Empty Set: “NULL Set” This type of set will look like { }= 0, It is a subset of every set. ~∀ xx ~ε 0]: Nothing is in the empty set. ∀ [0 c S]: Null set is in the set S. s The size or cardinality of a set B, |B|, is the number of elements in B. B = {7, 24, 42} |B| = 3 How to write the Cartesian product of two sets B & C. BxC = {(x, y) | (x ε B) Λ (y ε c)} B = {Red, Yellow} C = {7, 24, 42} BxC = {(Red, 7), (Red, 24), (Red, 42), (Yellow, 7), (Yellow, 24), (Yellow, 42)} BUC = {x | (x ε B) U (x ε C)} B∩C = {x | (x ε B) Λ (x ε C)} B C Discreet Math for Computing Aaron Maynard Timothy Farage February 15 2016 Let S be a set * The Power Set of S, P(S) = {All Subsets of S} B = {7, 24, 42} P(B) = {0, {7}, {24}, {42}, {7, 24}, {7, 42}, {24, 42}, {7, 24, 42}} ^ This contains a total of eight sets |P(B)| = 2|B| Ending Accounts Subsets can be explained through binary strings of length |B|. A set is said to be normal if the set does not contain itself. Test 1 will cover sections 1.1, 1.3, 1.4, 1.5, 1.7, 2.1, and 2.2. This test will also account for 1/3 of our final grade. Good luck everyone!


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