Scientific Computing CS 412 الحوسبة العلمیة عال 412

Scientific ComputingCS 412

العلمیة الحوسبة412عال

Lecture 4: Numbers and setsBy

I.Safa Alawneh

Numbers and setsThe 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 setsAn Irrational Number is a real number

that cannot be written as a simple fraction.

Irrational means not Rational

Examples:

Real Numbers are just numbers like: 1, 12.38 , -0.8625 ,3/4, √2, 1998

Numbers and sets

Representing NumbersIn computer systems, real numbers are

usually represented explicitly by floating-point numbers or symbolic or rule-based representation.

Representing Numbers

Representing Numbers

VectorsMany 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

Representing Vectors

Representing of functions (Explicit)

Representing of functions (Implicit)

Parametric Representing of functions

Parametric Representing of functions