COS 423 Lecture 1 Counting in Binary Amortized and Worst-Case Efficiency
... k. Let Φ = n mod 2k. Each add increases Φ by one, unless cost is k + 1 or more. (We call the add expensive.) In this case n mod 2k = 2k – 1, so Φ decreases by 2k – 1. This can happen at most n/2k times out of n: Φ = n - e2k ≥ 0, where e = #expensive adds. ...
... k. Let Φ = n mod 2k. Each add increases Φ by one, unless cost is k + 1 or more. (We call the add expensive.) In this case n mod 2k = 2k – 1, so Φ decreases by 2k – 1. This can happen at most n/2k times out of n: Φ = n - e2k ≥ 0, where e = #expensive adds. ...
Module 6 Chapters 10 and 11 Continued Fractions and Fibonacci
... A continued fraction is a way to represent numbers that are improper fractions or, in some cases, transcendental numbers. A continued fraction takes a whole LOT of room on a page so we quickly move to an alternate representation. For example: ...
... A continued fraction is a way to represent numbers that are improper fractions or, in some cases, transcendental numbers. A continued fraction takes a whole LOT of room on a page so we quickly move to an alternate representation. For example: ...
IOSR Journal of Mathematics (IOSR-JM)
... N.B. This is equation represents the general extension for cube of all real numbers when and where it is represented in terms of its Scindo Fragments. The brackets and braces here do not mean any tuples or sets. The brackets ( ) says that the algebraic operations should be done from inner most to ou ...
... N.B. This is equation represents the general extension for cube of all real numbers when and where it is represented in terms of its Scindo Fragments. The brackets and braces here do not mean any tuples or sets. The brackets ( ) says that the algebraic operations should be done from inner most to ou ...
Infinite Sets
... infinite set is one that is not finite. Example A = 1, 2, 3 is a finite set. B = n ∈ ℕ : n > 3 is an infinite set. A set A is a subset of the set B if every element of A is also an element of B. The set A is a proper subset of B is every element of A is an element of B but there are elements of ...
... infinite set is one that is not finite. Example A = 1, 2, 3 is a finite set. B = n ∈ ℕ : n > 3 is an infinite set. A set A is a subset of the set B if every element of A is also an element of B. The set A is a proper subset of B is every element of A is an element of B but there are elements of ...
Addition and Subtraction
... The above set model motivates the following definition for addition of whole numbers. Definition. Let a = n (A) and b = n(B) where A and B are two finite disjoint sets. Then a + b = n(A B). The whole numbers a and b are called addends and the result a + b is called the sum. Important Note. The set ...
... The above set model motivates the following definition for addition of whole numbers. Definition. Let a = n (A) and b = n(B) where A and B are two finite disjoint sets. Then a + b = n(A B). The whole numbers a and b are called addends and the result a + b is called the sum. Important Note. The set ...