Join Peggy Fisher for an in-depth discussion in this video Cardinality, disjointness, and partitions, part of Programming Foundations: Discrete Mathematics.
- [Voiceover] Understanding Cardinality,…Disjointness, and Partitions.…Cardinality is the number of elements in a set.…It is defined only for finite sets.…What would be the cardinality of a set…containing all the letter in the English alphabet?…If you said 26, you're right.…When working with sets, we say that two sets are disjoint…if they have no elements in common.…In other words, if the intersection…of the sets is the empty set.…Examples of disjoint sets include:…students enrolled in Discreet Mathematics at 10:05…and students enrolled in Spanish at 10:05.…
Another example would be…people living full time on the East Coast…and people living full time on the West Coast.…These sets do not have any elements in common.…A set partition includes all disjoint subsets…of a set that when combined make it whole.…If we have two disjoint sets, one is the vowels…and the other is the consonants, in the English alphabet,…These are two partitions of the whole set…which is the English alphabet.…Here we have two sets.…
What would be the cardinality of set A?…
This course relies on an open-source SML (standard machine language) library to demo the concepts behind discrete math. Peggy Fisher shows you how to manipulate sets of data, write proofs and truth tables, analyze data sequences, and visualize data using graph theory. Challenges at the end of every chapter allow you to test your knowledge. By the end of the course, you should be able to make the leap from theory to using discrete math in practice: saving time and resulting in code that's cleaner and easier to maintain in the long run.
- Real-world discrete math
- Objects as sets
- Set notation and operations
- Standard machine language (SML) setup
- Working with data types, strings, and functions in SML
- Analyzing data sequences
- Writing truth tables
- Identifying and evaluating predicates
- Validating arguments
- Writing proofs: subset, conditional, and biconditional proofs
- Visualizing data with graphs
- Advanced discrete math techniques
Skill Level Intermediate
1. Discrete Math Uses
3. Setting Up SML
4. Analyzing Data Sequences
5. Effective Arguments and Defensible Decisions
6. Proofs Made Easy
7. Advanced Discrete Math Topics
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