In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets that can be well-ordered. They were introduced by the mathematician Georg Cantor and are named after the symbol he used to denote them, the Hebrew letter aleph. The cardinality of the natural numbers is (read aleph-nought or aleph-zero; the term aleph-null is also sometimes used), the next larger cardinality of a well-orderable set is aleph-one then and so on. Continuing in this manner, it is possible to define a cardinal number for every ordinal number as described below. The concept and notation are due to Georg Cantor,who defined the notion of cardinality and realized that infinite sets can have different cardinalities. The aleph numbers differ from the infinity commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"), or as an extreme point of the extended real number line. (Wikipedia).
What is the definition of scientific notation
👉 Learn about scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the number of digits up to t
From playlist Scientific Notation | Learn About
Visualizing decimal numbers and their arithmetic 67 | Arithmetic and Geometry Math Foundations
This video gives a precise definition of a decimal number as a special kind of rational number; one for which there is an expression a/b where a and b are integers, with b a power of ten. For such a number we can extend the Hindu-Arabic notation for integers by introducing the decimal form
From playlist Math Foundations
Converting scientific notation
👉 Learn how to convert numbers from scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the nu
From playlist How to Convert Scientific Notation to a Number
Learn how to write a number our from scientific notation
👉 Learn how to convert numbers from scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the nu
From playlist How to Convert Scientific Notation to a Number
Calculus 1: Ch 5.1 Derivative of e^x and lnx (3 of 24) What is the Number e?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the number “e”. e=2.718218284590..., “e” is called the natural number” because in nature things tend to increase and decrease according to that number. Some of the examples of that inc
From playlist CALCULUS 1 CH 5.1 DERIVATIVES e^x AND ln x
Irrational Numbers - What are they?
Learn what an irrational number is in this free math video tutorial by Mario's Math Tutoring. 0:07 What is an Irrational Number 0:11 What is an Integer 0:35 Example of a Rational Number 7 1:02 Example of How a Repeating Decimal is Rational 1:26 Example 1 is Square Root of 7 Rational? 1:40
From playlist Algebra 1
Ex: Linear Equation Application with One Variable - Number Problem
This video provides and example of how to solve a number problem using a linear equation with one variable. One number is a multiple of the other. The difference is a constant. Find the two numbers. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Whole Number Applications
Support Vsauce, your brain, Alzheimer's research, and other YouTube educators by joining THE CURIOSITY BOX: a seasonal delivery of viral science toys made by Vsauce! A portion of all proceeds goes to Alzheimer's research and our Inquisitive Fellowship, a program that gives money and resour
From playlist Knowledge
👉 Learn how to convert numbers from scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the nu
From playlist How to Convert Scientific Notation to a Number
My video on Sesame Studios: https://www.youtube.com/watch?v=BTjAiyyG2sw The Curiosity Box by Vsauce: https://www.curiositybox.com/ LINKS TO SOURCES BELOW! My twitter: https://twitter.com/tweetsauce My instagram: https://www.instagram.com/electricpants DONG: https://www.youtube.com/dong M
From playlist Knowledge
Does Infinite Cardinal Arithmetic Resemble Number Theory? - Menachem Kojman
Menachem Kojman Ben-Gurion University of the Negev; Member, School of Mathematics February 28, 2011 I will survey the development of modern infinite cardinal arithmetic, focusing mainly on S. Shelah's algebraic pcf theory, which was developed in the 1990s to provide upper bounds in infinit
From playlist Mathematics
A road to the infinities: Some topics in set theory by Sujata Ghosh
PROGRAM : SUMMER SCHOOL FOR WOMEN IN MATHEMATICS AND STATISTICS ORGANIZERS : Siva Athreya and Anita Naolekar DATE : 13 May 2019 to 24 May 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The summer school is intended for women students studying in first year B.A/B.Sc./B.E./B.Tech.
From playlist Summer School for Women in Mathematics and Statistics 2019
Proof some infinities are bigger than other infinities
Yes, this video references The Fault in our Stars by John Green.
From playlist Doodling in Math and more | Math for fun and glory | Khan Academy
How many kinds of infinity are there?
A lot. List with links: http://vihart.com/how-many-kinds-of-infinity-are-there/
From playlist Doodling in Math and more | Math for fun and glory | Khan Academy
Algebra - Ch. 4: Exponents & Scientific Notation (21 of 33) Write Numbers in Scientific Notation 3
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and show how to write numbers in scientific notation: 10^0=1, 10^1=10, 10^-1=0.1, 10^2=100, 10^-2=0.01,... 284.6=?, 0.0245=?, 3125000=? -0.0042=?... in scientific notation. (Part 3) To donate
From playlist ALGEBRA CH 4 EXPONENTS AND SCIENTIFIC NOTATION
The efficiency misnomer | Size does not matter | What does the number of parameters mean in a model?
How important is the number of parameters in deep learning models? But what about other measures like FLOPs or speed/throughput? ► Check out our sponsor Aleph Alpha 👉 https://www.aleph-alpha.de/ ! Follow them on Twitter: Aleph__Alpha Paper 📜: Dehghani, Mostafa, Anurag Arnab, Lucas Beyer,
From playlist The Transformer explained by Ms. Coffee Bean
Introduction to the Cardinality of Sets and a Countability Proof
Introduction to Cardinality, Finite Sets, Infinite Sets, Countable Sets, and a Countability Proof - Definition of Cardinality. Two sets A, B have the same cardinality if there is a bijection between them. - Definition of finite and infinite sets. - Definition of a cardinal number. - Discu
From playlist Set Theory
Hexadecimal to Octal Conversion
This number systems tutorial explains how to do a hexadecimal to octal conversion. Subscribe: https://www.youtube.com/channel/UCEWpbFLzoYGPfuWUMFPSaoA?sub_confirmation=1 Access to Premium Videos: https://www.patreon.com/MathScienceTutor https://www.facebook.com/MathScienceTutoring/
From playlist Number Systems
Laura Fontanella: Reflection of stationary sets and the tree property at ℵω2+1
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Logic and Foundations