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  2. Round-off error - Wikipedia

    en.wikipedia.org/wiki/Round-off_error

    Compared with the fixed-point number system, the floating-point number system is more efficient in representing real numbers so it is widely used in modern computers. While the real numbers are infinite and continuous, a floating-point number system is finite and discrete. Thus, representation error, which leads to roundoff error, occurs under ...

  3. Number - Wikipedia

    en.wikipedia.org/wiki/Number

    In mathematics, the notion of number has been extended over the centuries to include zero (0), [3] negative numbers, [4] rational numbers such as one half (), real numbers such as the square root of 2 and π, [5] and complex numbers [6] which extend the real numbers with a square root of −1 (and its combinations with real numbers by adding or ...

  4. Floating-point arithmetic - Wikipedia

    en.wikipedia.org/wiki/Floating-point_arithmetic

    For example, the number 2469/200 is a floating-point number in base ten with five digits: / = = ⏟ ⏟ ⏞ However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits. The nearest floating-point number with only five digits is 12.346.

  5. Real number - Wikipedia

    en.wikipedia.org/wiki/Real_number

    In mathematics real is used as an adjective, meaning that the underlying field is the field of the real numbers (or the real field). For example, real matrix, real polynomial and real Lie algebra. The word is also used as a noun, meaning a real number (as in "the set of all reals").

  6. Floor and ceiling functions - Wikipedia

    en.wikipedia.org/wiki/Floor_and_ceiling_functions

    In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]

  7. Integer - Wikipedia

    en.wikipedia.org/wiki/Integer

    Historically the term was used for a number that was a multiple of 1, [10] [11] or to the whole part of a mixed number. [12] [13] Only positive integers were considered, making the term synonymous with the natural numbers. The definition of integer expanded over time to include negative numbers as their usefulness was recognized. [14]

  8. Rounding - Wikipedia

    en.wikipedia.org/wiki/Rounding

    Rounding to a specified power is very different from rounding to a specified multiple; for example, it is common in computing to need to round a number to a whole power of 2. The steps, in general, to round a positive number x to a power of some positive number b other than 1, are:

  9. Construction of the real numbers - Wikipedia

    en.wikipedia.org/wiki/Construction_of_the_real...

    An axiomatic definition of the real numbers consists of defining them as the elements of a complete ordered field. [2] [3] [4] This means the following: The real numbers form a set, commonly denoted , containing two distinguished elements denoted 0 and 1, and on which are defined two binary operations and one binary relation; the operations are called addition and multiplication of real ...