Basic properties of real numbers JEANS MURILLO

Basic Properties of Real Numbers
Real numbers have several basic properties that are fundamental in mathematics. Here is a summary of the most important ones:
1. Commutative Property
Addition: a+b=b+aa+b=b+a Multiplication: a×b=b×aa×b=b×a
2. Associative Property
Addition: (a+b)+c=a+(b+c)(a+b)+c=a+(b+c) Multiplication: (a×b)×c=a×(b×c)(a×b)×c=a×(b×c)
3. Distributive Property
Multiplication over addition: a×(b+c)=(a×b)+(a×c)a×(b+c)=(a×b)+(a×c)
4. Identity Property
Addition: a+0=aa+0=a Multiplication: a×1=aa×1=a
5. Inverse Property
Addition: For every real number aa, there exists a number −a−a such that a+(−a)=0a+(−a)=0
Multiplication: For every real number a≠0a=0, there exists a number 1aa1​ such that a×1a=1a×a1​=1
6. Closure Property
Addition: The sum of two real numbers is a real number.
Multiplication: The product of two real numbers is a real number.
These properties are essential for understanding and working with real numbers in various areas of mathematics.