In computer programming, an enumerated type (also called enumeration, enum, or factor in the R programming language, and a categorical variable in statistics) is a data type consisting of a set of named values called elements, members, enumeral, or enumerators of the type. The enumerator names are usually identifiers that behave as constants in the language. An enumerated type can be seen as a degenerate tagged union of unit type. A variable that has been declared as having an enumerated type can be assigned any of the enumerators as a value. In other words, an enumerated type has values that are different from each other, and that can be compared and assigned, but are not specified by the programmer as having any particular concrete representation in the computer's memory; compilers and interpreters can represent them arbitrarily. For example, the four suits in a deck of playing cards may be four enumerators named Club, Diamond, Heart, and Spade, belonging to an enumerated type named suit. If a variable V is declared having suit as its data type, one can assign any of those four values to it. Although the enumerators are usually distinct, some languages may allow the same enumerator to be listed twice in the type's declaration. The names of enumerators need not be semantically complete or compatible in any sense. For example, an enumerated type called color may be defined to consist of the enumerators Red, Green, Zebra, Missing, and Bacon. In some languages, the declaration of an enumerated type also intentionally defines an ordering of its members; in others, the enumerators are unordered; in others still, an implicit ordering arises from the compiler concretely representing enumerators as integers. Some enumerator types may be built into the language. The Boolean type, for example is often a pre-defined enumeration of the values False and True. Many languages allow users to define new enumerated types. Values and variables of an enumerated type are usually implemented with some integer type as the underlying representation. Some languages, especially system programming languages, allow the user to specify the bit combination to be used for each enumerator, which can be useful to efficiently represent sets of enumerators as fixed-length bit strings. In type theory, enumerated types are often regarded as tagged unions of unit types. Since such types are of the form , they may also be written as natural numbers. (Wikipedia).
Definition of an Injective Function and Sample Proof
We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil
From playlist Injective, Surjective, and Bijective Functions
Definition of a Surjective Function and a Function that is NOT Surjective
We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht
From playlist Injective, Surjective, and Bijective Functions
What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational
We've mentioned in passing some different ways to classify numbers, like rational, irrational, real, imaginary, integers, fractions, and more. If this is confusing, then take a look at this handy-dandy guide to the taxonomy of numbers! It turns out we can use a hierarchical scheme just lik
From playlist Algebra 1 & 2
Injective, Surjective and Bijective Functions (continued)
This video is the second part of an introduction to the basic concepts of functions. It looks at the different ways of representing injective, surjective and bijective functions. Along the way I describe a neat way to arrive at the graphical representation of a function.
From playlist Foundational Math
What is an Injective Function? Definition and Explanation
An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez
From playlist Functions
This tutorial explains the different types of numbers commonly used in algebra. The number types discussed are counting, whole, integer, rational, irrational, and imaginary. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)
From playlist Basic Math
In this tutorial I cross the bridge between a standard algebraic function and products sets, as well as mappings. I show the three types of mappings, namely injective (one-to-one), surjective (onto), and their combination, a bijection.
From playlist Abstract algebra
Lesson 02_03 Abstract and concrete types
Download the notebook files as they are added at: http://www.juanklopper.com/computer-programming/ All types are either concrete (that is a type right at the bottom of the tree of types) or abstract (basically everything higher up the tree). Concrete types are what we work with. We can c
From playlist The Julia Computer Language
Easy Rust 080: Enumerate and how iterators are made
The enumerate method and how Rust puts iterators together. From this chapter: https://dhghomon.github.io/easy_rust/Chapter_37.html #rustlang Want to buy me a coffee? Do it here: https://www.buymeacoffee.com/mithridates
From playlist Easy Rust / Rust in a Month of Lunches: bite-sized Rust tutorials
Enumeration in C Programming | enum In C Language | C Programming For Beginners | Simplilearn
This video by Simplilearn will explain to you Enumeration in C Programming. enum In C Language Programming tutorial will help you learn enumeration definition in c, how to use enum. This C programming tutorial will cover both theoretical and practical demonstrations for a better learning e
From playlist C++ Tutorial Videos
Linux Essentials For Hackers - #8 - Enumerating Distribution & Kernel Information
Welcome to the Linux Essentials For Hackers series, where we will be covering the 20% you need to know to be efficient with Linux. In this video, we will be covering how to enumerate distribution & kernel information in Linux. This series is sponsored by Linode, use the link below to get
From playlist Linux Essentials For Hackers
DNS Enumeration Tutorial - Dig, Nslookup & Host
Hey guys! HackerSploit here back again with another video, in this video, I will be showing you how to use Dig, Nslookup & host to perform DNS enumeration/reconnaissance. Our Platforms: Hsploit: https://hsploit.com/ HackerSploit Forum: https://hackersploit.org/ HackerSploit Academy: https
From playlist Ethical Hacking & Penetration Testing - Complete Course
Unity - lesson 15 - coroutines
From playlist Unity game engine
(UPDATED) LaTeX Tutorial 4 - Creating Lists
In this updated tutorial, I show you how to use LaTeX to create numbered and bulleted lists. To follow along with this tutorial I recommend using one of the following: (1) Overleaf: https://www.overleaf.com/?r=b4398ca7&rm=d&rs=b (2) TexMaker: https://www.xm1math.net/texmaker/ Warning! If
From playlist LaTeX Tutorials (featuring Texmaker)
Swift 2 Tutorial | Swift 2 Optionals | Swift 2 Binding | Swift 2 Code Safety | Swift 2 Enumerations
This video explains the basic of Swift 2.0 programming. It talks about the concepts like Swift 2.0 Optionals, Swift 2.0 Binding, Swift 2.0 Enumerations and Swift 2.0 Code Safety Objectives and Outcomes of the video " - Create app - Understand the app creation process - Create a new class
From playlist iOS App Development Tutorial Videos
Introduction To Pentesting - Enumeration
In this video, I demonstrate how to perform service enumeration with Nmap scripts. The target box that is used in this video is Metasploitable2. Metasploitable is an intentionally vulnerable Linux virtual machine. This VM can be used to conduct security training, test security tools, and p
From playlist Ethical Hacking & Penetration Testing - Complete Course
Ethical Hacking Tutorial | Comprehensive Subdomain Enumeration | Session 03 | #cybersecurity
Don’t forget to subscribe! This ethical hacking tutorial series is about comprehensive subdomain enumeration. Through this tutorial series, I will be demonstrating how to install, configure and use different tools for subdomain enumeration. We will try to go through the following subdom
From playlist Comprehensive Subdomain Enumeration
Nmap - OS And Service Version Scanning
In this video, I demonstrate how to perform OS and service version scanning and detection with Nmap. Nmap is a free and open-source network scanner created by Gordon Lyon. Nmap is used to discover hosts and services on a computer network by sending packets and analyzing the responses. Nmap
From playlist Ethical Hacking & Penetration Testing - Complete Course
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra