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Numbers - Zero to Infinity

Multiplication table
of
(maximum 24)
1 x
2 x
3 x
4 x
5 x
6 x
7 x
8 x
9 x
10 x
11 x
12 x
13 x
14 x
15 x
16 x
17 x
18 x
19 x
20 x
21 x
22 x
23 x
24 x
The most common number system types are:
Decimal number system (Base- 10)Input Decimal number
Binary number system (Base- 2)
Octal number system (Base-8)
Duodecimal base 12:
Hexadecimal number system (Base-16)
Our number system is a decimal system, or base ten system, meaning it's built powers of ten. Most number systems around the world use base ten, the origin of this system is likely based on hand counting: most people have ten fingers, and so we have ten digits. Aside from the number of fingers belonging to the median human, there's nothing particularly special about ten. We can use any whole number larger than one as a base, and get a perfectly good number system.

Computers are built around binary, or base two. Processors and operating systems are 32 bit or 64 bit since these are powers of two. Since binary is hard for humans to directly read, computer scientists and engineers often look at raw computer code represented in base eight octal, or base sixteen hexadecimal. Since eight and sixteen are powers of two (8 = 2 × 2 × 2, and 16 = 2 × 2 × 2 × 2), blocks of binary code are nicely translatable into these bases.

Suppose we lived in a world in which humans evolved to generally have four fingers on each hand, instead of five. It's pretty likely that we would have adopted an octal, or base eight, system, using powers of eight instead of powers of ten. In octal, we have eight digits — 0, 1, 2, 3, 4, 5, 6, and 7 — and now place values are based on powers of eight. The octal number 10 represents the number 8 in decimal. The octal 100 represents 8 × 8, or 64. 1000 is 8 × 8 × 8, or 512.

The hexadecimal system (also known as base 16) is a positional notation numeral system using twelve as its base. Any group of four bits translates into a hexadecimal digit: 0011 becomes a 3, and 1010 becomes 10, which is usually represented in hexadecimal as a capital A.

The Septimal system (also known as base 7) is a positional notation numeral system using 7 as its base. Examples are Weeks time keeping and music letter notation.

The duodecimal system (also known as base 12) is a positional notation numeral system using twelve as its base. The origin of the duodecimal system is typically traced back to a system of finger counting based on the knuckle bones of the four larger fingers. Using the thumb as a pointer, it is possible to count to 12 by touching each finger bone, starting with the farthest bone on the fifth finger, and counting on. In this system, one hand counts repeatedly to 12, while the other displays the number of iterations, until five dozens, i.e. the 60, are full. This system is still in use in many regions of Asia. Historically, units of time in many civilizations are duodecimal. There are twelve signs of the zodiac, twelve months in a year, and the Babylonians had twelve hours in a day

Zero to Infinity

zero is a complete absence and infinity is a complete lack of absence. That means Zero & infinity are two sides of the same coin. Everything (∞) is nothing (o), with a twist.
  1. Mathematics was developed to count definite things, starting with one. zero represents no things or nothing.
  2. Zero is a start number and Infinity is end number, while both defy measurement. Are Zero and Infinity just concepts?
  3. Between complexity of zero and infinity, number system is straightforward.
  4. Before God, nothing existed and God is defined as the starting point. God has also been defined as infinitely more powerful, good, knowing and perfection.
  5. Out of zero comes the infinite universe (or Big Bang). Nothing is a probability wave, of nothing and everything (nothing=everything)
  6. Zero and Infinity are the limits of human thinking.
  7. The Infinite is one of the most intriguing ideas in which the human mind has ever engaged.

More about Zero

  1. Some of the properties of zero:
  2. Zero is even (not odd, not neutral)
  3. Zero is not a prime number (smallest prime number is 2)
  4. Zero is neither positive nor negative
  5. Zero is an integer
  6. If you add or subtract zero from any other number, the answer will always result in the other number.
  7. The concept of dividing by zero is fraught with illogical consequences and does not work.
  8. Numbers to the zero power always equal one.

Zero Vector - Zero dimension

  1. Zero vector or null vector is a vector which has zero magnitude and an arbitrary direction. If a vector is multiplied by zero, the result is a zero vector. The simplest example of a vector space is the trivial one: {0}, which contains only the zero vector.
  2. An illustration of a nildimensional space is a point. Zero-dimensional Polish spaces include the Cantor space and Baire space.The physical meaning of can be understood from the following examples.
  3. The displacement of a ball thrown up and received back by the thrower is a zero vector.
  4. The velocity vector of a stationary body is a zero vector.
  5. The acceleration vector of a body in uniform motion is a zero vector.
  6. Zero dimension also includes absence of time dimension. As time does not exist, past, present and future coexist simultaneously.
  7. Three dimensions is our "normal" space. Two dimensions is a plane "Flatland". One dimension is a "line-world". Zero dimension is "point-world", where everything happens in the same place.
  8. Zero dimensions is like a rip in spacetime, where there is no spacetime

More about Infinity

Ancient Indians and Greeks approached infinity as a philosophical concept. Many ancient cultures had various ideas about the nature of infinity. Indians used the number line with zero and infinity. Two Indian words for infinity are asaṃkhyata ("countless, innumerable") and ananta ("endless, unlimited"). The Indian mathematical text Surya Prajnapti (c. 4th–3rd century BCE) classifies all numbers into three sets: enumerable, innumerable, and infinite. Each of these was further subdivided into three orders:
Enumerable: lowest, intermediate, and highest
Innumerable: nearly innumerable, truly innumerable, and innumerably innumerable
Infinite: nearly infinite, truly infinite, infinitely infinite
The universe is infinite, by Thomas Digges in 1576. In 1584, Giordano Bruno proposed an unbounded universe, Infinite Universe, Innumerable suns and planets around them
The Mahavaipulya Buddhavatamsaka Sutra or Avatamsaka Sutra, contains a description of an "incalculable" number, known as the asamkhyeya (lie outside the bounds of human calculability). Asamkhyeya is defined as a particular power of a laksha.
  1. Infinity does not do anything.
  2. The sequence of natural numbers never ends, and is infinite. Infinity is not a real number.
  3. Infinity is only an idea of something that has no end.
  4. Infinity does not grow and it is already and always fully formed. "endless", or "boundless"
  5. A Googol is 1 followed by one hundred zeros (less than infinity)
  6. Infinity is explored in articles such as the Ultimate, the Absolute, God, and Zeno's paradoxes.
  7. Three types of infinities are mathematical infinity; physical infinity; and a philosophical infinity.
  8. The infinite is an elusive concept, full of paradoxes and controversies. People look for precision, certainty, objectivity, and effectiveness in modeling things around us. Our bodies and our experiences are finite. We have never experienced or seen infinity.
  9. Philosophers have speculated about the nature of the infinite, such as Zeno of Elea, who proposed many paradoxes involving infinity, and Eudoxus of Cnidus, who used the idea of infinitely small quantities in his method of exhaustion. Modern mathematics uses the general concept of infinity in the solution of many practical and theoretical problems, such as in calculus and set theory, and the idea also is used in physics and the other sciences.
  10. In mathematics, "infinity" is often treated as a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as either a natural or a real number.
  11. A pre-Socratic Greek philosopher who lived in Miletus, used the word apeiron which means infinite or limitless. Mathematical infinity also comes from Zeno of Elea who is known for his paradoxes.

Some more on numbers

The concept of zero is essential to a system that’s at the basis of modern computing: binary numbers. Modern-day digital computers operate on the principle of two possible states, ‘on’ and ‘off’. The ‘on’ state is assigned the value ‘1’, while the ‘off’ state is assigned the value ‘0’. Or, zero. In the 2nd or 3rd Centuries BCE by a musicologist named Pingala, used this.

Two

In binary system, 2 = 10. So from single state to 2 states and generating large varieties by repeating the process. The number two is a symbolic representation of the state of duality which we experience objectively through our minds and the senses. It also symbolizes Purusha and Prakriti (God and Nature), Brahman and Atman, the knower and the known, the subject and the object, the doer and the deed, cause and effect, the right and wrong, knowledge and ignorance, life and death, etc

Three or Trinity

The number 3 is a prime number, and the first odd prime number.
The Trinity based on roles: Brahma is the creator. Vishnu is the preserver. Siva is the destroyer.
We are body - mind - spirit/soul
It was also the number of time – past, present, future;
Three worlds of heaven, earth and the hell;
Triple qualities of sattva, rajas and tamas;
Three layers of nature, light, fire and darkness;
Three states of being immanent, transcendent and the absolute;
Three worlds of heaven, earth and the hell;
Three phases of life, young age, middle age and old age;
Three paths to self-realization, the path of knowledge, the path of love and the path of action;
The triple control of control of body, mind and action or thought, word and deed;

Four

Four is the smallest composite number.
4**2 = 2**4
A circle divided by 4 makes right angles and four quadrants. Because of it, four (4) is the base number of the plane (mathematics).
A solid figure with four faces as well as four vertices is a tetrahedron, and 4 is the smallest possible number of faces (as well as vertices) of a polyhedron.
The god Brahma has four faces, may be indicating ability to see all 4 directions.
The aims of life (purusharthas) are four, dharma (righteousness), artha (wealth), kama (desire) and moksha.(salvation).
The stages (ashrama) in life are four: the age of studentship (brahmacharya), the age of householder (grihasta), the age of retirement (vanaprastha) and the age of ascetic (renunciation).
There are four ages or yugas: Golden, Silver, Bronze, and Iron (Satya, Dvapara, Treta and Kali)
The symbolic meanings of the number four are linked to those of the cross and the square.

Five

5 is the first safe prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime. 5 is the smallest Pythagorean triple (3, 4, 5)
Humans, and many other animals, have 5 digits on their limbs. Five elements: Ether (akasa); earth; Air (vayu); Agni (fire); and Water (jalam)
The senses are five in number: skin, eyes, nose, ears and tongue.

Six

6 is the smallest positive integer which is neither a square number nor a prime number. Six is the second smallest composite number; its proper divisors are 1, 2 and 3. Since six equals the sum of its proper divisors, six is the smallest perfect number, Granville number, and -perfect number.
6 represents 6 points forming hexagon, by intersection of two equal triangles
The mind is the sixth sense organ, with six faculties: reason, emotion, thought, awareness, knowledge and intelligence, and six enemies or impurities: lust, anger, greed, pride, delusion and envy.

Seven

Highest single digit prime number, which cannot be divided by any other number other than 1 and themselves.
7 is the only Number "that can divide "Infinitely" - infinitely, or "Infinite number of times"
1/7 = 0.142857 142857 142857 ....
2/7 = 0.285714 285714 285714 ....
3/7 = 0.428571 428571 428571 ....
4/7 = 0.571428 571428 571428 ....
5/7 = 0.714285 714285 714285 ....
6/7 = 0.857142 857142 857142 ....

Eight

8 can be halved successively till it reduces to 1.

number 9

9 = 3*3 (3 squre, smallest magic square)

The human body is considered as a city of nine gates which correspond with the nine openings (two eyes, two ears, two nostrils, navel and two excretory openings).

Ten

First 4 numbers totals 10 (1+2+3+4=10)
Ten is the first double digit number formed by the coming together of one and zero.

Twelve 12

12 is a composite number with four divisors (2, 3, 4 and 6).
12 Knuckles in a hand
12 Gods, 12 Disciples, 12 Tribes and the Zodiac of 12 months, rashis and so on.

Eighteen 18

18 a manifestation of 9, is a composite number, with large number of divisors being 1, 2, 3, 6 and 9. Three of these divisors (3, 6 and 9) add up to 18, hence 18 is a semi perfect number. 18 is the only number that equals twice the sum of its decimal digits.

Twenty-seven

27 is the value of the expression n^n, where n=3.
27 54 108 216 432 Harshad number series
27 is also a decagonal number.

60 and Sexagesimal system

60 is convenient for division by 2,3,4,5 and 6.
That way one can express fraction of 60 in whole numbers.
60 = 12 (Knuckles in a hand) * 5 (fingers in a hand)
The sexagesimal system of measurement is based on the number sixty. There are sixty seconds in a minute, sixty minutes in a hour. When we measure angles, we use the sexagesimal to express units in degrees, minutes and seconds. This method of measurement familiar to both the Indian and Mesopotamian cultures.
Sexagesimal system may be based in large part upon the observation of the planets, specifically Jupiter and Saturn. After every sixty years, Jupiter and Saturn will return to the same relative place in the zodiac.
The sixty years cycle of Jupiter and Saturn gives rise to another interesting number. In a sixty year period, Jupiter will complete five circuits of the zodiac and Saturn will complete two circuits. The combined individual cycles equal seven which is also the total number of visible planets plus the two luminaries.

Number 108 is LCM of 27 and 12

108 is a Harshad (means "great joy") number, which is an integer divisible by the sum of its digits (1+0+8 = 9)
The number 108 appears often in Hindu and Buddhist philosophy. 27 constallations and each one has 4 directions or 4 parts, and 27 * 4 = 108
9 corresponds to grahas and 12 to rassi and 9 * 12 = 108
Sun is approx 108 times the diameter of the Earth. The distance from the Sun to the Earth is approx 108 times the diameter of the Sun. Distance of the Moon from the Earth is approx 108 times the diameter of the Moon.
Silver represent the moon and atomic weight is 108.
There are a 108 marmas in the body.

Number 360

360 is a highly composite number
The smallest number divisible by every natural number from 1 to 10 except 7.
A circle is divided into 360 degrees for the purpose of angular measurement.
This choice of unit allows round angle to be divided into equal sectors measured in integer degrees rather than fractional degrees. 360 is the sum of two twin primes (179 + 181).
one year is close to 360 days, making it equal to 12 months (30*12).

Number 432

The number 432 = (2^4)*(3^3).
Equals 2 to the power of 4 multiplied by 3 to the power of 3.
432 is a Harshad number
It was consifered as magic number for astronomical calculations.
Kalacakra calendar in use, 60 year cycle starting with Prabhava, is by Pandita Somanatha of Kashmir/Himalayas, in 367 CE. Vernal equinox of 367 CE is Prabava Varsham. He further developed sexa decimal system. The earth's axis wobble that causes the precession of the equinoxes is approximately 25,920 years or 432 sixty year cycles.

Number 252 and 2520

252 is a Harshad number in base 10. Divisible by 1, 2, 3, 4, 6, 7, 9.
2520 is the smallest number divisible by all integers from 1 to 10, i.e., it is their least common multiple.
It is the product of five consecutive numbers, namely 3×4×5×6×7
2520=7*30*12 - 7 day week 30 days a month and 12 month
It is a Harshad number in all popular bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 16.

Infinity

Infinite and Zero are two boundaries.
The first unenumerable number was constructed using effectively a recursive construction. Still the highest enumerable number has not been attained.
Five different types of infinity: infinite in one direction, infinite in two directions, infinite in area, infinite everywhere and perpetually infinite.
The set of real numbers (or even complex numbers) does not include infinity. It’s not a number, but a symbol representing a particular kind of non-number. It’s either the “end” of a process that never ends (limits), or it’s a marker indicating something didn’t “converge” (series).
As a concept “infinity” is pre-historic. Indian scriptures reserve infinity, as attributes of almighty. It represents eternal time & space. Infinity make us accept of our limitations and feel humble in a good way. The Ouroboros or Lemniscate, meaning ‘ribbon’, by ancient Greeks, is an ancient symbol depicting a serpent biting its own tail. It represents the infinite immortality, continuity, and eternal return.
  • 1729 is the smallest number expressible as the sum of two cubes in two different ways. 1729 is the sum of the cubes of 10 and 9. Cube of 10 is 1000 and the cube of 9 is 729. Both the cubes, therefore, add up to 1729. 1729 is now known as the Ramanujan-Hardy number.
  • 2520 is a special number because it is divisible by all integers no from 1 to 10. 2520 is the smallest number divisible by all integers from 1 to 10, i.e., it is their least common multiple.