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This lecture focuses on the fundamental concepts of numbers and sets critical to scientific computing. We explore various number sets, including natural numbers (N), integers (Z), rational numbers (Q), and irrational numbers. The presentation details how real numbers are represented in computer systems, emphasizing floating-point representations and other symbolic methods. Additionally, we examine the distinction between scalar and vector quantities, highlighting the importance of accurate function representation in computing. This foundation aids in understanding computational methods and their applications in science.
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Scientific ComputingCS 412الحوسبة العلمیةعال 412 Lecture 4: Numbers and sets By I.SafaAlawneh
Numbers and sets • The set of natural numbers, denoted N, is the set of non-negative whole numbers: N= { 0,1,2,3 …..} • The set of integers, Z, contains the signed whole numbers including zero: Z= { …..,-2,-1,0,1,2, ……} • The set of rationals, Q, also include numbers with fractions: Q = { p/q: p, q€ Z ,q≠ 0}
Numbers and sets • An Irrational Number is a real number that cannot be written as a simple fraction. • Irrational means not Rational • Examples:
Numbers and sets • Real Numbers are just numbers like: 1, 12.38 , -0.8625 ,3/4, √2, 1998
Representing Numbers • In computer systems, real numbers are usually represented explicitly by floating-point numbers or symbolic or rule-based representation.
Vectors • Many quantities can be measured or reported using a single number: time, distance… • These are called Scalar quantities. • There are many phenomena that cannot use single scalar: a position in space
