# What is Numbers: Definition and 1000 Discussions

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any number using a combination of ten fundamental numeric symbols, called digits. In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, a numeral is not clearly distinguished from the number that it represents.
In mathematics, the notion of a number has been extended over the centuries to include 0, negative numbers, rational numbers such as one half

(

1
2

)

{\displaystyle \left({\tfrac {1}{2}}\right)}
, real numbers such as the square root of 2

(

2

)

{\displaystyle \left({\sqrt {2}}\right)}
and π, and complex numbers which extend the real numbers with a square root of −1 (and its combinations with real numbers by adding or subtracting its multiples). Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic, a term which may also refer to number theory, the study of the properties of numbers.
Besides their practical uses, numbers have cultural significance throughout the world. For example, in Western society, the number 13 is often regarded as unlucky, and "a million" may signify "a lot" rather than an exact quantity. Though it is now regarded as pseudoscience, belief in a mystical significance of numbers, known as numerology, permeated ancient and medieval thought. Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of many problems in number theory which are still of interest today.During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers, and may be seen as extending the concept. Among the first were the hypercomplex numbers, which consist of various extensions or modifications of the complex number system. In modern mathematics, number systems (sets) are considered important special examples of more general categories such as rings and fields, and the application of the term "number" is a matter of convention, without fundamental significance.

View More On Wikipedia.org
1. ### Can Natural Numbers m and n Satisfy x + 1/m < y - 1/n?

Let x, y ∈ R be such that x < y. Prove that there exist natural numbers m and n such that x +1/m < y −1/n?
2. ### I What is the role of geometry and dimensional operations?

As I was thinking about understanding the nature of multiplication and division, understanding the nature of numbers, I thought about the idea that there is something beyond multiplication and repeated addition. Then I thought about dimensional multiplication operations, such as area and volume...
3. ### B A conjecture on conjectures

Any set of a series of numbers consisting of increasing integer members, all of which are determined by a common proposition or characteristic, will always be infinite in size. Examples… Prime numbers Mersenne primes Odd perfect numbers(if they exist) Zeroes of the Zeta function Regardless...
4. ### Where does the mark scheme get these numbers from?

Q4B Mark scheme My working
5. ### A Explicit example of two complex numbers for double cover U(1) of SO(2) for a specified angle

I'm trying to find an explicit example showing exactly how the U(1) “circle group” of complex numbers double-covers 2D planar rotations R(θ) that form the rotation group SO(2). There are various explanations available online, some of which are clear but seem to be at variance with other...
6. ### A Omniscience principle and generic convergent sequence

I’m looking for someone to explain the first two equations in this article. I’ve got a good grip on it, but missing any sort of live feedback. https://www.cs.bham.ac.uk/~mhe/papers/omniscient-journal-revised.pdf Thanks, Oliver
7. ### Inequalities With negative numbers and switching x -- therefore switching the sign

My attempt: 4>19-3x Subtract 19 from both sides: -15 > -3x Divide both sides by -3: 5 > x Switch sides (change sign): x < 5 ! But Maths Genie tells me the answer is x>5 Where have I gone wrong?