A Few Fundamental Concepts and Principles of Mathematics

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Natural or Counting Numbers: 1,2,3,4,5, etc… Infinite Set

Whole Numbers: 0,1,2,3,4, etc… Infinite Set

Positive & Negative or Integers: …-3,-2,-1,0,+1,+2,+3… Infinite Set

Rational Numbers: Integers, Repeating and Terminating Decimals,

Proper and Improper Fractions,

Irrational Numbers: Non-Terminating and Non-Repeating Decimals

Numbers like: Pi = 3.14159… e = 2.71828…

Real Numbers: All Rational and All Irrational Numbers

Imaginary Numbers: Numbers with Negative Roots: “-i”, “-1”, “-i”, “+1”etc…

Complex Numbers: Binary combinations of Real and Imaginary Numbers.

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Properties of Mathematics:

Closure Property:	A + B = C	A * B = C
Commutative Property:	A + B = B + A	A * B = B * A
Associative Property:	A+(B+C) = (A+B)+C	A*(B*C) = (A*B)*C
Identity Property:	A + 0 = A	A * 1 = A
Inverse Property:	(+A) + (-A) = 0	(A) * (1/A) = 1
Distributive Property:	A(B+C)=(A*B)+(A*C)	(B+C)A=(BA)+(CA)

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Axioms of Algebra:

Addition Axiom: Equals added to equals results in equals

Subtraction Axiom: Equals subtracted to equals results in equals

Multiplication Axiom: Equals multiplied to equals results in equals

Division Axiom: Equals divided by equals results in equals

Exponential Axiom: Equals raised to an equal power results in equals

Root Axiom: Equals raised to an equal root results in equals

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Tom Love Malone College Fall 2003