Browse Definitions:
Definition

# irrational number

An irrational number is a real number that cannot be reduced to any ratio between an integer p and a natural number q . The union of the set of irrational numbers and the set of rational numbers forms the set of real numbers. In mathematical expressions, unknown or unspecified irrationals are usually represented by u through z. Irrational numbers are primarily of interest to theoreticians. Abstract mathematics has potentially far-reaching applications in communications and computer science, especially in data encryption and security.

Examples of irrational numbers are 2 1/2 (the square root of 2), 3 1/3 (the cube root of 3), the circular ratio pi, and the natural logarithm base e . The quantities 2 1/2 and 3 1/3 are examples of algebraic numbers. Pi and e are examples of special irrationals known as a transcendental numbers. The decimal expansion of an irrational number is always nonterminating (it never ends) and nonrepeating (the digits display no repetitive pattern).

If x and z are irrationals such that x < z, then there always exists an irrational y such that x < y < z. The set of irrationals is "dense" like the set Q of rationals. But theoretically, the set of irrationals is "more dense." Unlike Q , the set of irrationals is nondenumerable. There are more nonterminating, nonrepeating decimals than is possible to list, even by implication. To prove this, suppose there is an implied list of all the nonterminating, nonrepeating decimal numbers between 0 and 1. Every such number consists of a zero followed by a decimal point, followed by an infinite sequence of digits from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Suppose the elements of the list are denoted x 1, x 2 , x 3, ... and the digits in the numbers are denoted a ii. The list can be written like this:

x 1 = 0. a 11 a 12 a 13 a 14 a 15 a 16 ...
x 2 = 0. a 21 a 22 a 23 a 24 a 25 a 26 ...
x 3 = 0. a 31 a 32 a 33 a 34 a 35 a 36 ...
x 4 = 0. a 41 a 42 a 43 a 44 a 45 a 46 ...
x 5 = 0. a 51 a 52 a 53 a 54 a 55 a 56 ...
x 6 = 0. a 61 a 62 a 63 a 64 a 65 a 66 ...
...

Even though we don't know the actual values of any of the digits, it is easy to imagine a number between 0 and 1 that can't be in this list. Think of a number y of the following form:

y = 0. b 11 b 22 b 33 b 44 b 55 b 66 ...

such that no b ii in y is equal to the corresponding a ii in the list. The resulting number y is nonterminating and nonrepeating, is between 0 and 1, but is not equal to any x i in the list, because there is always at least one digit that does not match.

The non-denumerability of the set of irrational numbers has far-reaching implications. Perhaps most bizarre is the notion that "not all infinities are created equal." Although the set of rationals and the set of irrationals are both infinite, the set of irrationals is larger in a demonstrable way.

This was last updated in October 2016

#### Join the conversation

Send me notifications when other members comment.
this site is amazing....
Cancel
Circumference of Circle / Diameter = Goba, 6283185306 / 2000000000 = 3.141592653 Constant of Goba means Pi is Rational Number.
Hon. Chancellor, Vice-Chancellor, President, Dean, Chairman Board of Studies, Principal, Head of Department, Mathematics, Physics, Philosophy, Science and Astronomy of schools, colleges, educational institutes, educational boards, mathematical institutes, scientific institutes, universities, and the universities listed in the Q S (Quacquarelli Symonds) scholars and scientists in INDIA and WORLD,

Reference:
Editorial of International Journal of Shantaram Janorkar Foundation of Mathematics, Science and Spiritual. – Edition – 1, 15 September, 2015, Volume – 1, Issue – 1, ISO 9001:2008, ISSN (P): 2454-5236, ISSN (O): 2454-633X, Title Code: MAHBIL06980/13/1/2014-TC / For Books - ISO 9001:2008, ISBN: 978-81-930845-0-2, (English and Marathi). (FREE DOWNLOAD from www.sbjanorkar.com)
(i) (Circumference of a Circle / Diameter = Goba, 6283185306 / 2000000000 = 3.141592653 Constant of Goba). The Self - Proving Theorem of Goba and its Explanation on the Basis of a Formula.
(ii) E=Mm2 Which means Energy = Mass x (Speed of Mass)2, Speed of Light = 22,32,00,00,000 Mile/Second. (Twenty two Hundred and Thirty two Cores Mile/per Second).
(iii) 504,866,505,707,712,000 (Mile)³/Second The Extent of solar system.
(iv) The Theorem of the Formula for the Explanation for the Creation of the Cosmos in the Large Hadron Collider Machine.
(v) Point - The Theorem of Existence of Point and its Aspect.
(vi) The Distance Between Shining Lightening as well as Thundering Cloud and The Earth.
(vii) To do Research on the Research Done by Shantaram Bapurao Janorkar we Expect to Operation from World Educational Institute, Universities, Scholars, Scientists.

http://www.sbjanorkar.com/booksd.html

This international journal has been launched in memory of my father and researcher late Mr. Shantaram Bapurao Janorkar by “Shantaram Janorakar Foundation of Mathematics” to scientifically establish the research carried out by him on the various topics of Mathematics and I have put my best efforts in this work disregarding my family and my children’s future. This is the biggest sacrifice made by me and this sacrifice has been done by me for my country. This sacrifice has been done for the students all over the whole world to enable them to achieve the true and real knowledge. I have been doing my research work at different levels for the last 18 years. To really establish this research, on 11 December, 2011, I received valuable guidance from Hon.Prof.Dr.T.M.Karade (D.Sc., D.Sc., Ex. Vice-Chancellor, Indiana University, Raipur, Ex. Dean, Faculty of Science, Nagpur University, Nagpur) and to scientifically establish this research I am also receiving valuable guidance from Hon.Prof.Dr.Shriram B.Patil (Ex. Head, Department of Mathematics, Ex. Chairman, Board of Studies in Mathematics, Ex. Dean, Faculty of Science, Mumbai University, Mumbai) Through this guidance, I found many ways about how I should scientifically establish all this research and by this Institute I have launched the journal “International Journal of Shantaram Janorkar Foundation of Mathematics, Science and Spiritual.” Through this medium I have been preparing various papers on this research in English and Marathi languages and publishing them serially in this journal. I have prepared the papers on this research and I have tried to convert them into scientific and mathematical language without leaving the basic core of the research topics which were invented by my father and researcher late Mr. Shantaram Bapurao Janorkar and keeping intact the meaning of his thoughts through scientific approach, I have compiled the theorems on various subjects and prepared research papers on these theorems. I have prepared these research papers by using various systematic methods and I have tried to explain everything and made use of methods which are easy and quick to understand for you. In case you do further studies on this research and prepare papers on the same we shall certainly publish them in this journal free of charge and you will be honored with a citation and award. I desire to publish this journal in all regional, national and international languages.
This journal is in ‘Print/CD-ROM/Online’ formats. I have been trying to deliver this journal to the scholars and scientists of 511 universities of India and to the scholars and scientists of 10,877 universities all over the world. I sincerely request to honorable scholars and scientists to continue further my present work. There is such a great extent of knowledge in this research work that the yet to be in completed research will be completed with this research and logic and the world will get to know the real and true knowledge and you can put new theorems before the world created through this research. To help this real and true knowledge put forward before the world is the very primary objective of my efforts. It is said that time and tide waits for none; ‘Death’ is the eternal truth for all living beings on earth. Hence, it is utmost essential to put forth my research paper in front of the world. I feel, after my death, there will be nobody to put forth or present this research paper in front of the world.
In Geometry, the symbol of measurement accepted (World Official) by the world community of scientist is degree and this same degree is the root, evidence, origin and base of the entire research done by my father late Mr. Shantaram Bapurao Janorkar. The base of this entire research is measure of circle of 36 Degree. By transforming this research which is originally in Marathi language, into scientific and mathematical language I am publishing serially all the papers on this research in an international journals. To begin with, I have first prepared the papers on the theorems:
 The Self - Proving Theorem of Goba and its Explanation on the Basis of a Formula (Circumference of a Circle / Diameter = Goba, 6283185306 / 2000000000 = 3.141592653 Constant of Goba). (Goba Cha Swayamshidha Sidhanta Wa Sutracha Aadharacha Spastikaran (Wartul Parigh / Wyas = Goba, 6283185306 / 2000000000 = 3.141592653 Goba Cha Sthirank), (In Marathi).
 Point - The Theorem of Existence of Point and its Aspect. (Bindu – Binducha Asthitwachi Shidhatha Wa Swarup, (In Marathi).
 E = Mm2 Which means Energy = Mass x (Speed of Mass)2, Speed of Light = 22,32,00,00,000 Mile/per Second. (Twenty two Hundred and Thirty two Cores Mile/per Second). (E=Mm2 Mhanajhach Shakati = Wastuman x Wastumanacha Wegacha Varga, Prakashacha Wega = 22,32,00,00,000 Mail / Prati Second (Bavis Abja Batish Koti Mail / Prati Second, (In Marathi).
 The Distance Between Shining Lightening as well as Thundering Cloud and The Earth. (Chakaknari Wig Aani Gadgadnara Megha yanche Pruthavi Pasun Aantar, (In Marathi),
 The Theorem of the Formula for the Explanation for the Creation of the Cosmos in the Large Hadron Collider Machine.
 The Theorem of the Extent of the Solar systems. (Surya malecha wyapacha shidhanta, (In Marathi).
 A Personality called Shantaram Bapurao Janorkar. (Shantaram Bapurao Janorkar Yak Wyaktimahatava, (In Marathi),
 The Establishment of Shantaram Janorkar Foundation of Mathematics to Create a New History in Mathematics, Science, Philosophy & Spiritual. (Ganit, Vidhyan, Thatvadhyan Vaa Adhyatma Madhye Yek Navin Etihas Ghadavinya Karita Shantaram Janorkar Foundation of Mathematics Chi Sthapana, (In Marathi),
 To do Research on the Research Done by Shantaram Bapurao Janorkar we Expect to Operation from World Educational Institute, Universities, Scholars, Scientists. (Shantaram Bapurao Janorkar Yancha Sanshodhanavar Sanshodhan Honyakarita Vishavatil Shaishanik Savunstha, Vidhyapithe, Scholars, Shastradhyan Kadun Sahakaryachi Aaphekasha, (In Marathi), in mathematical language and in the transforming the research papers on “Goba” in mathematical language by making some modifications, Hon.Prof.D.T.Solanke has helped me while in the translation work of this research work from Marathi to English, I received cooperation from Hon.Mr.Vikram K. More and Hon.Prof.Dr.T.M.Karade provided me the guidance on how should the first paragraph of the research paper on “Goba” be read. The paragraph reads like this The value of an irrational number pi is determined from the ancient times up to the modern super computer era. In this paper author Late Shri Shantaram Bapurao Janorkar has conjunctured the rational number , Christened “GOBA” by introducing some concept with references to a circle is nomenclature is like π (Pi), but it is not an irrational number. Its value is computed as 3.141592653
If you look at this research with the unselfish vision of a scholar, scientist (researcher) and if you carefully read the work published in this publication, you will easily understand the research work and ways for further research on this work can be found. In this research many new theorems have been established, different new methods have been found and in the same way many new theorems and methods will be found. I have made a deep study on this research and while deciding on which methods should be included in this paper and which methods are easier, I have came across some theorems in addition to this theorem and they follow as: For example,
 The Theorem of the Evolution or Creation of the Cosmos and Speed. (Wishavachi uttapathi kinva nirmiti vaa vegacha shidhanta, (In Marathi).
 The theorem of the Evolution or Creation of the Radius, straight radius, arc radius and diameter of Circle and the Circumference of Circle. (Wartul vaa wartul parighachi thrigha, saral thrigha, kauns thrigha Aani wyasacha uttapathi kinva nirmiti cha shidhanta, (In Marathi).
 The Theorem of the total number of planets-stars, solar systems and galaxies in the cosmos. (Wishava madhil graha-tare, Surya mala Aani Aakashagaangan - cha shidhanta, (In Marathi).
 The Theorem of the Extent of the Cosmos. (Wishavacha vyapacha shidhanta, (In Marathi).
 The Theorem of the definite Period taken by the Creation of the entire Cosmos (Saampurna Wishava nirmitila lagalelya nishyit welyecha shidhanta, (In Marathi).
 The Theorem of the Extent of the Black Hole in the Centre of Galaxies. (Aakashagaangan chya Madhya bhagi Aaslelya krushan vivaracha vyapacha shidhanta, (In Marathi).
 The Theorem of the Mental Speed (Manachya vegacha shidhanta, (In Marathi).
 The Theorems of the Numbers, Vedic 16 Vowels, Vedic 36 Consonants and Their Symbolic Signs. (Aanka, vaidik 16 Swar, vaidik 36 vyanjane vaa thyanchya syanketik chinhyancha shidhanta, (In Marathi). With this,
 Squarization of a Circle = 5605 x 5605 = 31416025 / 10000000 = 3.14160250 (Wartulache chaurasikaran = 5605 x 5605 = 31416025/10000000 = 3.14160250, (In Marathi). In spirituality on the basis of mathematical rules,
 Om - The Scientific Verification of Om and its Aspect. (Om - Om Che Wiadhyanik Drustya Shidhatha Wa Swarup, (In Marathi).
 Soul-The Verification of the Existence of Soul, Its Aspect and Nomenclature. (Aatmaa - Aatmaaya Chya Asthitwachi Shidhatha, Swarup Wa Namkaran, (In Marathi).
I will try to publish in the next issue the further papers on this theorem. Hon.Mr.Dr.T.M.Karade, Prof.Dr.Shriram B.Patil, Prof.Dr.Kishor S.Adhav, Prof.Dr.S.D.Katore, Prof.Mr. D.T.Solanke have been regularly providing valuable guidance to me and therefore, I am very much grateful to them and I shall remain grateful to them forever. In case you find any difficulty in understanding the research papers published in this journals please send your queries in writing on the editorial address, I shall sincerely strive to solve them. You can contact me round the clock on phone or in person. This journal is being published by Om Publications, Mahan and it is ISSN, ISBN, RNI and ISO 9001:2008 certified.
All the people, schools, colleges, educational institutes, educational boards, mathematical institutes, scientific institutes, universities, and the universities listed in the QS (Quacquarelli Symonds) scholars, scientists, researchers all over the world can subscribe annually free of charge from the web site www.sbjanorkar.com. You can download the e-copy of this international journal in PDF format from the web site www.sbjanorkar.com and I sincerely request you cooperate me in sharing it with your friends, teachers, students, schools, colleges, education institutes, education boards, mathematical institutes, scientific institutes, all the students of an university and people through your email as well as social sites such as Facebook, Google Plus, WhatsUp, Twitter, LinkedIn. I dedicate the first issue of this journal to the memory of my father and the researcher of this entire work, late Mr. Shantaram Bapurao Janorkar, the valuable research done by him, his trust in education.
 Mr.Dhananjay S.Janorkar (Chief Editor)

The Function of Publication and Dedication to the World of the International Journal through Organization of Shantaram Janorkar Foundation of Mathamatics, Mahan
On the occasion of the birth Anniversary of Late Mr. Shantaram Bapurao Janorkar, an International Journal of Shantaram Janorkar Foundation of Mathematics, Science and Spiritual, was published through Organization of Shantaram Janorkar Foundation of Mathamatics, Village MAHAN - 444 405 Tq. Barshitakli Dist. Akola, (Maharashtra State), India. On 15/09/2015 at evening 5.00 P.m. at Mahan at the hands of Hon. Professor Dr. Kishor Aadhav, D.Sc., (Head, Department of Mathematics, Sant Gadage Baba Amaravati University, Amaravati) and dedication of this International Journal to the World was performed at the hands of Hon. Professor Dr. S. D. Katore, (Chairman, Board of Studies in Mathematics, Sant Gadage Baba Amaravati University, Amaravati), Chief Guest was Hon. Professor Mr. D. T. Solanke, (Department of Mathematics, Sudhakar Naik & Umashankar Khetan College, Akola), The President of this function was Mr. Dhananjay S. Janorkar, (Founder President, Shantaram Janorkar Foundation of Mathamatics).
Along with this international journal, Mr. Dhananjay Shantaram Janorkar has determined 504,866,505,707,712,000 (Mile)³/Second The Extent of solar system and 160,704,000,000,000,000 (Mile)³/Second as diameter as per the principle of solar system invented by them. Along with this, numerous principle invention papers has been kept before the world through this International Journal and to investigate on this invention Mr. Dhananjay Shantaram Janorkar has created a new rostrum for global scholars like Ph. D. holders in respect of the same. The said international journal/Books can be downloaded free of cost at www.sbjanorkar.com on this web site. In the said programme Deputy Sarpanch of Mahan, Mr. Pramod Bhadange, Smt. Sulbhabai Shantaram Janorkar, Ex-Chairman, Panchayat Samati Barshitakli also Secretary of organization Mrs. Jija Dhananjay Janorkar, Mr. Dilip Lande Guruji, Mr. Sanjay Ambarkar, Mr. Prabhakar Janorkar, Mr. Uday Janorkar, Mr. Suvarnesh Janorkar, Dr. Nitin Janorkar, Mayur Jangle, Rishikesh Janorkar, Jay Janorkar and Janorkar family were present at the function.

Shantaram Janorkar Foundation of Mathematics,
Village MAHAN - 444 405 Tq. Barshitakli Dist. Akola
Head Offices:- C/o R.T.Patil House, Near Saraswati
Akola - 444 404, (Maharashtra State), India.
Phone (Mob): 09021607450, 09226442256
E-mail: sjfomindia@gmail.com, ijosjfomss@gmail.com
www.sbjanorkar.com
http://www.sbjanorkar.com/booksd.html

Cancel

## SearchCompliance

• ### PCAOB (Public Company Accounting Oversight Board)

The Public Company Accounting Oversight Board (PCAOB) is a Congressionally-established nonprofit that assesses audits of public ...

• ### cyborg anthropologist

A cyborg anthropologist is an individual who studies the interaction between humans and technology, observing how technology can ...

• ### RegTech

RegTech, or regulatory technology, is a term used to describe technology that is used to help streamline the process of ...

## SearchSecurity

• ### email spam

Email spam, or junk email, is unsolicited bulk messages sent through email with commercial, fraudulent or malicious intent.

• ### distributed denial of service (DDoS) attack

A distributed denial-of-service attack occurs when an attack originates from multiple computers or devices, usually from multiple...

• ### application whitelisting

Application whitelisting is the practice of identifying applications that have been deemed safe for execution and restricting all...

## SearchHealthIT

• ### athenahealth Inc.

Based in Watertown, Mass., athenahealth Inc. is a leading vendor of cloud-based EHRs for small to medium-sized physician ...

• ### Affordable Care Act (ACA or Obamacare)

The Affordable Care Act (ACA) is legislation passed in 2010 that changed how uninsured Americans enroll in and receive healthcare...

• ### HIPAA Privacy Rule

The Standards for Privacy of Individually Identifiable Health Information, commonly known as the HIPAA Privacy Rule, establishes ...

## SearchDisasterRecovery

• ### disaster recovery as a service (DRaaS)

One approach to a strong disaster recovery plan is DRaaS, where companies offload data replication and restoration ...

• ### data recovery

Data recovery restores data that has been lost, accidentally deleted, corrupted or made inaccessible. Learn how data recovery ...

• ### disaster recovery plan (DRP)

A company's disaster recovery policy is enhanced with a documented DR plan that formulates strategies, and outlines preparation ...

## SearchStorage

• ### virtual memory

Virtual memory is a memory management capability of an OS that allows a computer to compensate for physical memory shortages by ...

• ### yottabyte (YB)

A yottabyte is a measure of theoretical storage capacity and is 2 to the 80th power bytes, or, in decimal, approximately 1,000 ...

• ### Kilo, mega, giga, tera, peta, exa, zetta and all that

Kilo, mega, giga, tera, peta, exa, zetta are among the list of prefixes used to denote the quantity of something, such as a byte ...

## SearchSolidStateStorage

• ### PCIe SSD (PCIe solid-state drive)

A PCIe SSD (PCIe solid-state drive) is a high-speed expansion card that attaches a computer to its peripherals.

• ### SSD caching

SSD caching, also known as flash caching, is the temporary storage of data on NAND flash memory chips in a solid-state drive so ...

• ### NVDIMM (Non-Volatile Dual In-line Memory Module)

An NVDIMM (non-volatile dual in-line memory module) is hybrid computer memory that retains data during a service outage.

## SearchCloudStorage

• ### RESTful API

A RESTful application program interface breaks down a transaction to create a series of small modules, each of which addresses an...

• ### cloud storage infrastructure

Cloud storage infrastructure is the hardware and software framework that supports the computing requirements of a private or ...

• ### Zadara VPSA and ZIOS

Zadara Storage provides block, file or object storage with varying levels of compute and capacity through its ZIOS and VPSA ...

Close