# Number, Numeric, Quantity

## About

A number is a mathematical object used to:

- and measure.

Example: When we are interested in the total number of each species of tortoise, or how many individuals there are per square kilometre.

This type of data is called commonly:

- numerical data
- or quantitative data.

The same number may be:

- (represented|expressed|written) in many numeral system (or system of numeration)
- classified by their properties in number system
- added to a field where most of the mathematical function can be applied.

## Why

Number Type | Equation they help to solve |
---|---|

Negative number | a + x = b, even when a > b |

Fractions | ax = b, when b is not divisible by a |

Reals | x² = 2 |

Complex numbers | x² = -1 |

## Notion

### Number System

Numbers can be classified into set, called number system.

The most common number system (ie number classification) are:

### Numeral System

Numbers can be expressed (ie written) into set, called numeral system (or system of numeration). It is a mathematical notation system for expressing numbers using digits (or other symbols).

Example of numeral system (ie number representation)]]:

- base 10: decimal in the (business|human) world
- (binary|bit) and hexadecimal in the (machine|computer) world
- Base 60: Babylonian for time and angle

### Number Storage

Numbers can be stored in:

However, since division almost immediately introduces infinitely repeating sequences of digits (such as 4/7 in decimal, or 1/10 in binary), the representation would be:

- truncated at some satisfactory size
- or else rational numbers would be used: a large integer for the numerator and for the denominator. But even with the greatest common divisor divided out, arithmetic with rational numbers can become unwieldy very quickly: 1/99 – 1/100 = 1/9900, and if 1/101 is then added the result is 10001/999900.

(From wiki/Arbitrary-precision_arithmetic)

### Field

A field is a collection of “numbers” with their operator: +, -, *, /

### Discrete / Continous

Quantitative variables can be further categorized as either:

- discrete: those that can only have set, integral values, or discrete variables,
- or continuous: those that can be a range of values, or continuous variables. Quantitative Variables can be a range of values, or continuous variables.

## Documentation / Related

- See java implement of Number: AtomicInteger, AtomicLong, BigDecimal, BigInteger, Byte, Double, DoubleAccumulator, DoubleAdder, Float, Integer, Long, LongAccumulator, LongAdder, Short