Abelian group theory | Elementary number theory | Algebraic number theory | Elementary mathematics | Ring theory
An integer is the number zero (0), a positive natural number (1, 2, 3, etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z or blackboard bold . The set of natural numbers is a subset of , which in turn is a subset of the set of all rational numbers , itself a subset of the real numbers . Like the natural numbers, is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, (rational) integers are algebraic integers that are also rational numbers. (Wikipedia).
Multiplying and Dividing Integers
From playlist Integers
Ex: Limits Involving the Greatest Integer Function
This video provides four examples of how to determine limits of a greatest integer function. Site: http://mathispower4u.com
From playlist Limits
Types Of Numbers | Numbers | Maths | FuseSchool
We all know what numbers are 1, 2, 3, 4, 5, …. Including negative numbers -1, -2, -3, -4, -5, ... But did you know that mathematicians classify numbers into different types… into a number system. Let’s start at the top with real numbers. They can be positive… negative… zero… decimals, frac
From playlist MATHS: Numbers
From playlist Computation with Integers
This video introduces integers, compares integers using inequality symbols, defines absolute value, and determine opposites of integers. Complete Video List: http://mathispower4u.yolasite.com/
From playlist Introduction to Integers
Graphing Calculator - Greatest Integer
Use the graphing calculator to find the greatest integer associated with andy real or complex number
From playlist Graphing Calculator - Basic Commands and Operations
Lecture 4 - Floors and Ceilings
This is Lecture 4 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2004.pdf More information may
From playlist CSE547 - Discrete Mathematics - 1999 SBU
Greatest Integer Function With Limits & Graphs
This calculus video tutorial explains how to graph the greatest integer function and how to evaluate limits that contain it. This video contains plenty of examples and practice problems evaluating limits with the greatest integer function using the help of a number line. Examples include
From playlist New Calculus Video Playlist
Consecutive Integers Word Problems - Even & Odd Examples
This algebra lesson math video tutorial explains how to solve consecutive integers word problems. It explains how to do it the simple way. This video contains plenty of examples and practice problems including even and odd consecutive integer problems.
From playlist GED Math Playlist
Direct Proofs: Beginner Examples (Even/Odd)
Let's prove some basic statements using the direct proof method! This is intended for beginners to direct proof or proof in general. Timestamps: 0:00 Introduction 00:50 Definitions 3:31 Example 1 8:14 Example 2 12:18 Example 3 15:53 Example 4 Thanks for watching! Comment below with quest
From playlist Proofs
Prove that x^2 + x is even for every integer x
Prove that x^2 + x is even for every integer x If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com Free Homework Help : https://mathsorcererforums.com/ My FaceBook Page: https://www.facebook.com/themathsorc
From playlist Math Proofs for Beginners
The sum of three consecutive integers plus 5 is 20. What are the numbers?
How to solve an algebra word problem involving consecutive integers. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, revi
From playlist GED Prep Videos
Introduction to Proof Methods!
The first video I've made on proof methods! I discuss what a proof is, give some general tips, show how to prove a conditional statement using the direct proof method, and use the direct proof method to do some very beginner friendly proofs! The goals of this video: 1. Help people underst
From playlist Proofs
Step-By-Step Guide to Proofs | Ex: product of two evens is even
How do you prove a mathematical claim? This video provides a step-by-step process to help you prove simple, direct proofs. We begin with the assumption, apply the definition, do some manipulations, apply the definition of the conclusion, and finish at the conclusion. We will investigate
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
CTNT 2022 - Algebraic Number Theory (Lecture 1) - by Hanson Smith
This video is part of a mini-course on "Algebraic Number Theory" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - Algebraic Number Theory (by Hanson Smith)
Rational and Irrational Numbers - N2
A review of the difference between rational and irrational numbers and decimals - including square rootes and fraction approximations of pi.
From playlist Arithmetic and Pre-Algebra: Number Sense and Properties
[ANT13] Dedekind domains, integral closure, discriminants... and some other loose ends
In this video, we see an example of how badly this theory can fail in a non-Dedekind domain, and so - regrettably - we finally break our vow of not learning what a Dedekind domain is.
From playlist [ANT] An unorthodox introduction to algebraic number theory