Numbers Definition and 9 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




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

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  1. F

    I Blending numbers

    i have not clue if this is the right place to ask if i had 2 numbers and i wanted to blend between them but instead of a linear way it was in an inverse square way.. how would that math go? so if i had A=1 and B=9 and wanted the number at 0.5 it would be 4.. or if i wanted the number at 0.85 it...
  2. Jarvis323

    A Choices of Axiomatic and Number Systems / Sets and Alternatives

    I know that the number systems we use are typically constructed from axiomatic set theory, and overall our choices along the way seam to have been largely informed by practical consideration (e.g. to resolve ambiguities, or do away with limitations). Today I randomly started to think deeper...
  3. J

    I decrypting this

    00110100 00110011 00100000 00110100 00111001 00100000 00110100 00110011 00100000 00110100 00110001 00100000 00110100 00110100 00100000 00110100 00110001 00100000 00110010 00110000 00100000 00110011 00110011 00100000 00110011 00110011 00100000 00110011 00110000 00100000 00110011 00110001
  4. Y

    Orbital/Spin angular momentum + magnetic quantum numbers

    Homework Statement A single electron atom has the outer electron in a 4f1 excited state. Write down the orbital and spin angular momentum quantum numbers and the associated magnetic quantum numbers for this state. Homework Equations I don't think there is any relevant equations. I think it...
  5. Bunny-chan

    Supremum and infimum of specific sets

    Homework Statement I'm in need of some help to be able to determine the supremum and infimum of the following sets:A = \left\{ {mn\over 1+ m+n} \mid m, n \in \mathbb N \right\}B = \left\{ {mn\over 4m^2+m+n^2} \mid m, n \in \mathbb N \right\}C = \left\{ {m\over \vert m\vert +n} \mid m \in...
  6. J

    B Solve 3 7 12 18 25 series

    Hi, I am trying to solve this series generally: the series: 3 7 12 18 25. i tried using x(n) = 3 + 4n. But this doesn't work.. Please help.
  7. Carlos Gouveia

    Fast car

    A car goes from repose (0 mph) to 50 mph in, say, 30 seconds. Math tells us that there is an infinite amount of numbers between 0 and 50 (or between any two other numbers). Therefore, isn't it "obvious" or "intuitive" that it would take a car an infinite amount of time to go from 0 mph to 50...
  8. M

    Can anyone explain me this?

    Homework Statement Let m be the number of numbers fromantic the set {1,2,3,...,2014} which can be expressed as difference of squares of two non negative integers. The sum of the digits of m is ... Homework Equations The Attempt at a Solution I got a solution from a magazine but I didn't...
  9. N

    N00b question about understanding what formulas are

    I am new to the world of Science & Mathematics but am eager to learn all I can. I go to my local library and open up books on the topic such as Physics, Engineering and Electronics and there are swathes of formulas all of which I don't understand. I stare at them wondering what keys they must...