Hypercomplex numbers

Multicomplex number

In mathematics, the multicomplex number systems are defined inductively as follows: Let C0 be the real number system. For every n > 0 let in be a square root of −1, that is, an imaginary unit. Then . In the multicomplex number systems one also requires that (commutativity). Then is the complex number system, is the bicomplex number system, is the tricomplex number system of Corrado Segre, and is the multicomplex number system of order n. Each forms a Banach algebra. G. Bayley Price has written about the function theory of multicomplex systems, providing details for the bicomplex system The multicomplex number systems are not to be confused with Clifford numbers (elements of a Clifford algebra), since Clifford's square roots of −1 anti-commute ( when m ≠ n for Clifford). Because the multicomplex numbers have several square roots of –1 that commute, they also have zero divisors: despite and , and despite and . Any product of two distinct multicomplex units behaves as the of the split-complex numbers, and therefore the multicomplex numbers contain a number of copies of the split-complex number plane. With respect to subalgebra , k = 0, 1, ..., n − 1, the multicomplex system is of dimension 2n − k over (Wikipedia).

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Conversion Arcs and 2,916,485,648,612,232,232,816 (MegaFavNumbers)

I'm sorry. The MegaFavNumbers playlist: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo

From playlist MegaFavNumbers

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A Short Tutorial on Computing Persistent Homology Using Spectral Sequences [Álvaro Torras Casas]

First, we review briefly the classical computation of persistent homology. Then we introduce the multicomplex and twisted differentials. Next we compute the persistent spectral sequence for a particular case, obtaining the persistence pairs as a result. Finally, we briefly review the block

From playlist Tutorial-a-thon 2021 Fall

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Multimeter Review / DMM Review / buyers guide / tutorial

A list of my multimeters can be purchased here: http://astore.amazon.com/m0711-20?_encoding=UTF8&node=5 In this video I do a review of several digital multimeters. I compare features and functionality. I explain safety features, number of digits, display count, accuracy and resolution. Th

From playlist Multimeter reviews, buyers guide and comparisons.

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1,010,010,101,000,011 - #MegaFavNumbers

This is my submission to the #megafavnumbers project. My number is 1010010101000011, which is prime in bases 2, 3, 4, 5, 6 and 10. I've open-sourced my code: https://bitbucket.org/Bip901/multibase-primes Clarification: by "ignoring 1" I mean ignoring base 1, since this number cannot be fo

From playlist MegaFavNumbers

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#MegaFavNumbers - 7,588,043,387,109,376 by Egi

87,109,376^2=7,588,043,387,109,376. The last 8 digits is the square root😀, it's called an automorphic number which n^2 ends with n

From playlist MegaFavNumbers

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How to multiply a two digit whole number by a three digit whole number

👉 You will learn how to multiply integers from one digit to multiple digits. When multiplying it is important to understand that multiplication is just repeated addition. However with multi-digit numbers we will follow a step by step process to find the product of the two numbers. 👏SUB

From playlist Integer Operations

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MegaFavNumbers: 1.5 Billion

#MegaFavNumbers What’s your Mega Favourite Number?

From playlist MegaFavNumbers

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#MegaFavNumbers - Largest number constructible from just one copy of the digits 1, 2, 3, and 4

#MegaFavNumbers #MegaFavNumber Should it have the 's' or not? After first publishing this, I noticed that videos tended to have the plural, including the first in the list. It doesn't make much sense for a single video to use the plural, but I think I have to in order to be picked up

From playlist MegaFavNumbers

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Ex 2: Multiply Complex Numbers

This video provides examples of how to multiply complex numbers. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com

From playlist Performing Operations with Complex Numbers

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How to multiply a two digit decimal from a three digit decimal

👉 You will learn how to multiply numbers in decimal form. We will work with decimals that are greater and less than one. When multiplying decimals it is important to line up the decimal point so that you keep the place values of the numbers. We will apply multi digit multiplication to f

From playlist How to multiply and divide decimals

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How is i equal to square root of -1?

What is 'i'? More importantly, what is a complex number? How are complex numbers relevant to the context of other familiar numbers? Chapters: 00:00 Introduction 01:46 Logo of Reals and Rationals 02:11 Expanding real numbers 03:25 Motivation using whole (natural) numbers 06:08 Planar numb

From playlist Summer of Math Exposition 2 videos

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Fun with Math: Surprises with Arithmetic and Numbers

Stephen Wolfram shows kids and adults some fun unique things you can do with math. All demonstrations powered by the Wolfram Language. Originally livestreamed at: https://twitch.tv/stephen_wolfram Follow us on our official social media channels: Twitter: https://twitter.com/WolframRese

From playlist Stephen Wolfram Livestreams

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How to understand the REAL NUMBER LINE - COLLEGE ALGEBRA

In this video we talk about natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. We also show the real number line and the inequalities less than and greater than. 00:00 Intro 00:29 Number system 04:53 Visual representation of numbers 07:37 Rea

From playlist College Algebra

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Real Numbers

This video provides a basic introduction into real numbers. It explains how to distinguish them from imaginary numbers. It also discusses the difference between rational and irrational numbers as well as integers, natural numbers, and whole numbers. Examples include repeating and non-re

From playlist New Algebra Playlist

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What are Isotopes?

This chemistry video tutorial answers the question - what are isotopes? Isotopes are substances that are composed of the same element but consist of different mass numbers and number of neutrons. They share the same atomic number and therefore the same number of protons. This video cont

From playlist New AP & General Chemistry Video Playlist

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Pascal's wager and real numbers

My entry for 3blue1brown's contest, talking about Pascal's wager and how it leads to interesting questions about (hyper)real numbers. A big shoutout to Grant for coming up with this wonderful idea. Link to Thierry Platinis channel for more on hyperreal numbers: https://www.youtube.com/cha

From playlist Summer of Math Exposition Youtube Videos

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Year 13/A2 Pure Chapter 0.1 (Subsets of Real Numbers, Representatives and Proof)

Welcome to the first video for year 13 (A2) Pure Mathematics! This video is part of a series of three that I've called Chapter 0, and is meant as a foundation for Year 13. The primary reasons for doing this are that the difficulty of Year 13 is markedly harder than Year 12 content, and al

From playlist Year 13/A2 Pure Mathematics

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My favorite proof of the n choose k formula!

The binomial coefficient shows up in a lot of places, so the formula for n choose k is very important. In this video we give a cool combinatorial explanation of that formula! Challenge Problems playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJGkzGsXMYQt8bi5ImYtiEMM Subscribe t

From playlist Challenge Problems

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Is the Sieve of Eratosthenese past its prime?

The Sieve of Eratosthenes is an amazing tool for teaching people about prime numbers and composite numbers but it's not without its limitations. I've tried to answer the question, 'Is there a better way of representing a sieve like this?' 0:00 Sieve of Eratosthenes In the first part of t

From playlist Summer of Math Exposition Youtube Videos

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#MegaFavNumbers How many combinations on the 4x4 and 5x5 Rubik's cubes?

#MegaFavNumbers 4x4: 7 401 196 841 564 901 869 874 093 974 498 574 336 000 000 000 5x5: 282 870 942 277 741 856 536 180 333 107 150 328 293 127 731 985 672 134 721 536 000 000 000 000 000 Video I mentioned: https://www.youtube.com/watch?v=fbejrvORXRA

From playlist MegaFavNumbers

Related pages

Clifford algebra | Corrado Segre | Split-complex number | Complex number | Dimension | Mathematics | Imaginary unit | Real number | Subalgebra | Zero divisor | Banach algebra | Bicomplex number