Search results
Results from the WOW.Com Content Network
For example, on the extended real number line, dividing any real number by infinity yields zero, [2] while in the surreal number system, dividing 1 by the infinite number yields the infinitesimal number . [3] [4]: 12 In floating-point arithmetic, any finite number divided by is equal to positive or negative zero if the numerator is finite.
Prime number: A positive integer with exactly two positive divisors: itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ... Composite number: A positive integer that can be factored into a product of smaller positive integers. Every integer greater than one is either prime or composite.
Fractions can be used to represent ratios and division. [1] Thus the fraction 3 / 4 can be used to represent the ratio 3:4 (the ratio of the part to the whole), and the division 3 ÷ 4 (three divided by four). We can also write negative fractions, which represent the opposite of a positive fraction.
[1] [3] For example, if a line is viewed as the set of all of its points, their infinite number (i.e., the cardinality of the line) is larger than the number of integers. [4] In this usage, infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object.
Kasner used it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics. To put in perspective the size of a googol, the mass of an electron, just under 10 −30 kg, can be compared to the mass of the visible universe, estimated at between 10 50 and 10 60 kg. [ 5 ]
Infinitesimals (ε) and infinities (ω) on the hyperreal number line (ε = 1/ω) In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinity-eth" item in a sequence.
In mathematics, the infinite series 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1.
where c 1 = 1 / a 1 , c 2 = a 1 / a 2 , c 3 = a 2 / a 1 a 3 , and in general c n+1 = 1 / a n+1 c n . Second, if none of the partial denominators b i are zero we can use a similar procedure to choose another sequence {d i} to make each partial denominator a 1: