Search results
Results from the WOW.Com Content Network
Notably, is the first uncountable cardinal number that can be demonstrated within Zermelo–Fraenkel set theory not to be equal to the cardinality of the set of all real numbers: For any natural number , we can consistently assume that =, and moreover it is possible to assume that is as least as large as any cardinal number we like.
Positive numbers: Real numbers that are greater than zero. Negative numbers: Real numbers that are less than zero. Because zero itself has no sign, neither the positive numbers nor the negative numbers include zero. When zero is a possibility, the following terms are often used: Non-negative numbers: Real numbers that are greater than or equal ...
Since the natural numbers have cardinality , each real number has digits in its expansion. Since each real number can be broken into an integer part and a decimal fraction, we get: c ≤ ℵ 0 ⋅ 10 ℵ 0 ≤ 2 ℵ 0 ⋅ ( 2 4 ) ℵ 0 = 2 ℵ 0 + 4 ⋅ ℵ 0 = 2 ℵ 0 {\displaystyle {\mathfrak {c}}\leq \aleph _{0}\cdot 10^{\aleph _{0}}\leq 2 ...
Integer overflow can be demonstrated through an odometer overflowing, a mechanical version of the phenomenon. All digits are set to the maximum 9 and the next increment of the white digit causes a cascade of carry-over additions setting all digits to 0, but there is no higher digit (1,000,000s digit) to change to a 1, so the counter resets to zero.
In general, if an increase of x percent is followed by a decrease of x percent, and the initial amount was p, the final amount is p (1 + 0.01 x)(1 − 0.01 x) = p (1 − (0.01 x) 2); hence the net change is an overall decrease by x percent of x percent (the square of the original percent change when expressed as a decimal number).
1698 (perhaps deriving from a much earlier use of middle dot to separate juxtaposed numbers) division slash (a.k.a. solidus ) 1718 (deriving from horizontal fraction bar, invented by Abu Bakr al-Hassar in the 12th century)
In mathematics, a negative number is the opposite of a positive real number. [1] Equivalently, a negative number is a real number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset.
A generalization of the self-descriptive numbers, called the autobiographical numbers, allow fewer digits than the base, as long as the digits that are included in the number suffice to completely describe it. e.g. in base 10, 3211000 has 3 zeros, 2 ones, 1 two, and 1 three. Note that this depends on being allowed to include as many trailing ...