In mathematics, the supernatural numbers, sometimes called generalized natural numbers or Steinitz numbers, are a generalization of the natural numbers. They were used by Ernst Steinitz in 1910 as a part of his work on field theory. A supernatural number is a formal product: where runs over all prime numbers, and each is zero, a natural number or infinity. Sometimes is used instead of . If no and there are only a finite number of non-zero then we recover the positive integers. Slightly less intuitively, if all are , we get zero. Supernatural numbers extend beyond natural numbers by allowing the possibility of infinitely many prime factors, and by allowing any given prime to divide "infinitely often," by taking that prime's corresponding exponent to be the symbol . There is no natural way to add supernatural numbers, but they can be multiplied, with . Similarly, the notion of divisibility extends to the supernaturals with if for all . The notion of the least common multiple and greatest common divisor can also be generalized for supernatural numbers, by defining and . With these definitions, the gcd or lcm of infinitely many natural numbers (or supernatural numbers) is a supernatural number.We can also extend the usual -adic order functions to supernatural numbers by defining for each . Supernatural numbers are used to define orders and indices of profinite groups and subgroups, in which case many of the theorems from finite group theory carry over exactly. They are used to encode the algebraic extensions of a finite field. Supernatural numbers also arise in the classification of uniformly hyperfinite algebras. (Wikipedia).
The Magical Fraction 1/999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999
The number 1/999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999 has the Fibonacci numbers in order for every group of 24 decimals. This video explains why the pattern emerges. (sources, proofs, and links below) Via Futility Closet: http://www.futilitycloset.com/2015/06/28/mad
From playlist Everyday Math
Imaginary numbers are any numbers that include the imaginary number i. A mix of imaginary and real numbers gives you what’s called a complex number. The primary reason we use imaginary numbers is to give us a way to find the root (radical) of a negative number. There’s no way to use real
From playlist Popular Questions
Tutorial - What is an imaginary number
http://www.freemathvideos.com In this video playlist you will learn everything you need to know with complex and imaginary numbers
From playlist Complex Numbers
What are Real Numbers? | Don't Memorise
Watch this video to understand what Real Numbers are! To access all videos on Real Numbers, please enroll in our full course here - https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=3YwrcJxEbZw&utm_term=%7Bkeyword%7D In this video, w
From playlist Real Numbers
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
What are Irrational Numbers? | Number System | Don't Memorise
Watch this video to know more about Rational numbers, Irrational Numbers, Real Numbers and Number System. To learn more about Irrational Numbers, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=CtRtXoT_
From playlist Irrational Numbers
There are a lot more numbers than I thought there were - MegaFavNumbers
A short video detailing my favorite number larger than 1 million! There are so many numbers out there it was hard to choose from, but I’m glad I could participate in the #MegaFavNumbers series
From playlist MegaFavNumbers
The Cognitive Basis of Superstition and Belief in the Supernatural
What is superstition, and what is the psychological basis behind it? What drives belief in the supernatural, and is there any evolutionary basis for it? Are we merely driven to detect patterns in chaos, or is there something more to it? Let's dig into this now! Children’s belief in an inv
From playlist Psychology
Supernatural thinking: Your brain’s anti-anxiety mode | Clay Routledge
This interview is an episode from The Well, our new publication about ideas that inspire a life well-lived, created with the John Templeton Foundation. Subscribe to The Well on YouTube ► https://bit.ly/thewell-youtube Up Next ► What kind of atheist are you? https://youtu.be/e246ClGyWgU I
From playlist Welcome to The Well
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
We discuss what imaginary numbers are and how they are part of the larger set of complex numbers in this free math video tutorial by Mario's Math Tutoring. This is a nice introduction to working with i. We also go through some examples. 0:26 A Hierarchy of Different Types of Numbers 1:03
From playlist Imaginary & Complex Numbers
Richard Dawkins: 2 Flaws Plague Unscientific Belief, from Trump & Alt-Right to Religious Doctrine
2 Flaws Plague Unscientific Belief, from Trump & Alt-Right to Religious Doctrine New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge -------------------------------------------------------------------------
From playlist Richard Dawkins | Big Think
Why humans believe “everything happens for a reason” | Clay Routledge
This interview is an episode from The Well, our new publication about ideas that inspire a life well-lived, created with the John Templeton Foundation. Subscribe to The Well on YouTube ► https://bit.ly/thewell-youtube Up Next ► Michio Kaku: Is God a mathematician? https://youtu.be/Kfq50Vs
From playlist Welcome to The Well
September 29, 2008 lecture by Eugenie Scott for the Stanford Continuing Studies course on Darwin's Legacy (DAR 200). Dr. Scott explores the evolution vs. creationism debate and provides an argument for evolution. The lecture is concluded with a panel discussion with Brent Sockness and Je
From playlist Lecture Collection | Darwin's Legacy
AQA English Literature Paper 1 Section B: 2023 Edition
An updated guide to the 19th century novel section of the AQA GCSE English Literature exam. Download the free worksheet accompanying this video at mrbruff.com/worksheets 0:06 paper overview 0:28 assessment objective 1 1:24 the highest marks 1:54 assessment objective 2 7:20 assessment obj
From playlist AQA GCSE English Literature Paper 1
Student Exemplar: Freud, Nietzsche, Id & Binary Opposition in 'A Christmas Carol'
Buy my revision guides in paperback on Amazon*: Mr Bruff’s Guide to ‘A Christmas Carol’ https://amzn.to/37wH2hp Mr Bruff’s Guide to GCSE English Language https://amzn.to/2GvPrTV Mr Bruff’s Guide to GCSE English Literature https://amzn.to/2POt3V7 AQA English Language Paper 1 Practice Pa
From playlist Student Exemplars
Anthony Aguirre - Did God Create Multiple Universes?
What is the extent of God's creation? If there are multiple universes, did God create each of them? If an infinite number of universes, did God create all of them? Click here to watch more interviews on God and multiple universes http://bit.ly/2mlpQCF Click here to watch more interviews
From playlist Big Questions About God - Closer To Truth - Core Topic
Looking for Patterns in AQA English Literature Paper 1
Buy my revision guides in paperback on Amazon*: Mr Bruff’s Guide to GCSE English Language https://amzn.to/2GvPrTV Mr Bruff’s Guide to GCSE English Literature https://amzn.to/2POt3V7 AQA English Language Paper 1 Practice Papers https://amzn.to/2XJR4lD Mr Bruff’s Guide to ‘Macbeth’ htt
From playlist AQA GCSE English Literature Paper 1
From playlist a. Numbers and Measurement