Set Notations and Definitions in CSE Discussions
Explore the concepts of sets, n-tuples, Cartesian products, and set-wise concatenation in computer science engineering discussions. Learn about defining sets, properties of n-tuples, and practical examples to deepen your understanding.
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Presentation Transcript
CSE 20 Discussion Week 1 TA Yuanjun Dastin Huang
Logistics - What is Discussion Session about? - Have a question regarding homework/etc.? - Today s agenda
Notations & Definitions - Set - {} - Order/repetition doesn t matter - n-tuple - () - Fixed length - Order/repetition matters! - String - Order/repetition matters! - Arbitrary finite length - Set Definition - Roster method - Set builder notation - Recursive definition - Cartesian Product - ? ? = {(?,?):? ?,? ?} - Creates set of tuples - Set-wise Concatenation - ? ? = {??|? ? ??? ? ?} - Creates set of strings
Set - Property - {} - Empty set denoted as ? - Order/repetition doesn t matter - 3 Ways to define a set - Roster method - Set builder notation - Recursive definition - Example - The set which contains all natural number from 1 to 5 - The set which contains all even number from 1 to 5
n-tuple - Property - () - Order/repetition does matter - Example - (1, 1) (1) - {1, 1} {1} - (1, 2) (2, 1) - {1, 2} {2, 1}
Cartesian Product - Property - ? ? = {(?,?):? ?,? ?} - Creates set of tuples - Example - ? = 0,1 ,? = 2,3 - ? ? = - Question: A and B both have 2 elements, how many tuples are there in ? ?? - ? = 0,1 ,? = 0,1 - ? ? =
Set-wise Concatenation - String - Order/repetition matters! - Arbitrary finite length - Empty string denoted as - Example - Alphabet = {x, y} - A = x ,B = {?} - A B =? - 1ststep: specify {?|? ?}, {?|? ?} - 2ndstep: write down A B according to definition
