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2 hours ago · The Syracuse function is the function f from the set I of positive odd integers into itself, for which f(k) = k ′ (sequence A075677 in the OEIS). Some properties of the Syracuse function are: For all k ∈ I, f(4k + 1) = f(k). (Because 3(4k + 1) + 1 = 12k + 4 = 4(3k + 1).) In more generality: For all p ≥ 1 and odd h, f p − 1 (2 p h − 1 ...
1 day ago · The red set is an open set, the blue set is its boundary set, and the union of the red and blue sets is a closed set. In mathematics, an open set is a generalization of an open interval in the real line . In a metric space (a set along with a distance defined between any two points), an open set is a set that, along with every point P, contains ...
2 hours ago · Complex number. A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i2 = −1. In mathematics, a complex number is an element of a number system ...
1 day ago · Formal power series. In mathematics, a formal series is an infinite sum that is considered independently from any notion of convergence, and can be manipulated with the usual algebraic operations on series (addition, subtraction, multiplication, division, partial sums, etc.). A formal power series is a special kind of formal series, whose terms ...
2 hours ago · Ruler function. A ruler, marked in centimeters (top), and inches (bottom). The rising and falling pattern of vertical lines on the inch scale resembles the ruler function. In number theory, the ruler function of an integer can be either of two closely related functions. One of these functions counts the number of times can be evenly divided by ...
1 day ago · In computing, floating-point arithmetic ( FP) is arithmetic that represents subsets of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. Numbers of this form are called floating-point numbers. [1] : 3 [2] : 10 For example, 12.345 is a floating-point number in base ten ...
1 day ago · The likelihood function ( ) for the probability of a coin landing heads-up (without prior knowledge of the coin's fairness), given that we have observed HHT. Consider a simple statistical model of a coin flip: a single parameter that expresses the "fairness" of the coin.
