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Real Number system

STUDYYYYYY

QuestionAnswer
N Natural
W Whole
Z Integers
Q Rational
I Irrational
R Real
This applies to addition and multiplication, stating that the order of numbers doesn't change the result. For example, a+b=b+a and a×b=b×a Commutative Property:
This also applies to addition and multiplication, indicating that how numbers are grouped in parentheses doesn't affect the outcome. For example, (a+b)+c=a+(b+c) and (a×b)×c=a×(b×c) Associative Property:
This bridges addition and multiplication, showing that multiplying a number by a sum is the same as multiplying each addend individually and then adding the products. For example, a×(b+c)=(a×b)+(a×c) Distributive Property:
This describes the identity elements for addition and multiplication. For addition, the identity is 0, because any number plus 0 remains unchanged (a+0=a). For multiplication, the identity is 1, because any number times 1 remains unchanged (a×1=a) Identity Property:
This involves the additive and multiplicative inverses. The additive inverse is the number that, when added, results in zero (a+(−a)=0). The multiplicative inverse is the number that, when multiplied, results in one (a×1a=1, assuming a≠0) Inverse Property:
This property states that if the product of two numbers is zero, then at least one of the factors must be zero. In other words, for any numbers a and b, if a×b=0, then either a=0, b=0, or both. Zero Property (also called the Zero Product Property):
Created by: user-1774290
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