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Identify the properties of real numbers.
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http://www.math.com/school/subject2/lessons/S2U2L1GL.html
To identify the properties of real numbers, we can look at a few key concepts and characteristics. Here are some important properties of real numbers:
1. Closure Property: Real numbers are closed under addition and multiplication, meaning that if you add or multiply any two real numbers, the result will always be a real number.
2. Associative Property: Addition and multiplication of real numbers are associative operations. This means that when adding or multiplying three or more real numbers together, the grouping of the numbers does not affect the final answer. For example, (a + b) + c = a + (b + c) and (a * b) * c = a * (b * c).
3. Commutative Property: Addition and multiplication of real numbers are commutative operations. This means that changing the order of the numbers being added or multiplied does not affect the result. For example, a + b = b + a and a * b = b * a.
4. Identity Property: The real number 0 is the additive identity, meaning that adding 0 to any real number leaves the number unchanged. The real number 1 is the multiplicative identity, meaning that multiplying any real number by 1 leaves the number unchanged. For example, a + 0 = a and a * 1 = a.
5. Inverse Property: Every real number has an additive inverse and a multiplicative inverse. The additive inverse of a real number a is -a, such that a + (-a) = 0. The multiplicative inverse of a non-zero real number a is 1/a, such that a * (1/a) = 1.
6. Distributive Property: The distributive property states that multiplication distributes over addition. This means that for any real numbers a, b, and c, a * (b + c) = a * b + a * c.
These properties are fundamental to the nature of real numbers and form the basis for various mathematical operations and proofs.