Chapter 6: Rational Number Operations and Properties
... 6.1.2.1. Definition of a rational number: A number is a rational number if and only if it a a can be represented by a pair of integers, , where b ≠ 0 and represents the b b quotient a ÷ b 6.1.3. Using Fractions to Represent Rational Numbers 6.1.3.1. Fractions and Equivalent Fractions a 6.1.3.1.1. De ...
... 6.1.2.1. Definition of a rational number: A number is a rational number if and only if it a a can be represented by a pair of integers, , where b ≠ 0 and represents the b b quotient a ÷ b 6.1.3. Using Fractions to Represent Rational Numbers 6.1.3.1. Fractions and Equivalent Fractions a 6.1.3.1.1. De ...
Pigeonhole Principle
... Pigeonholes & subsequences • Can use the pigeonhole principle to show the existence of a subsequence of a certain length within a sequence of distinct integers • For a sequence of the form: a1, a2, … , aN a subsequence is a sequence of the form: ai1,ai2, … ,aim where 1<=i1< i2< … < im<=N • So if we ...
... Pigeonholes & subsequences • Can use the pigeonhole principle to show the existence of a subsequence of a certain length within a sequence of distinct integers • For a sequence of the form: a1, a2, … , aN a subsequence is a sequence of the form: ai1,ai2, … ,aim where 1<=i1< i2< … < im<=N • So if we ...
Discrete Mathematics - Lyle School of Engineering
... N : The set of all natural numbers (i.e.,all positive integers) Z : The set of all integers Z+ : The set of all positive integers Z* : The set of all nonzero integers E : The set of all even integers Q : The set of all rational numbers Q* : The set of all nonzero rational numbers Q+ : The set of all ...
... N : The set of all natural numbers (i.e.,all positive integers) Z : The set of all integers Z+ : The set of all positive integers Z* : The set of all nonzero integers E : The set of all even integers Q : The set of all rational numbers Q* : The set of all nonzero rational numbers Q+ : The set of all ...
Significant Figures
... In all numbers there are digits that are Significant & others are not Significant. Why should we be concerned which numbers are significant? ...
... In all numbers there are digits that are Significant & others are not Significant. Why should we be concerned which numbers are significant? ...
Internal representation of numbers in computers
... Rules for NaN, ±∞, etc. follow as above with the critical value of e being 2047 instead of ...
... Rules for NaN, ±∞, etc. follow as above with the critical value of e being 2047 instead of ...
Infinity
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.In mathematics, ""infinity"" is often treated as if it were a number (i.e., it counts or measures things: ""an infinite number of terms"") but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number; see 1/∞.Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.