Rules for Numbers
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چکیده
The real numbers are governed by a collection of rules that have to do with addition, multiplication, and inequalities. In the rules below, x, y, z 2 R. (In other words, x, y, and z are real numbers.) Rules of addition. • (x + y) + z = x + (y + z) (Law of associativity) • x + y = y + x (Law of commutativity) • x + 0 = x (Law of identity) • x + x = 0 (Law of inverses) Rules of multiplication. • (xy)z = x(yz) (Law of associativity) • xy = yx (Law of commutativity) • x1 = x (Law of identity) • If x 6 = 0 then 1 x x = 1 (Law of inverses) Distributive Law. There is a rule that combines addition and multiplication: the distributive law. Of all the rules listed so far, it's arguably the most important. • x(y + z) = xy + xz (Distributive Law) 6 Rules for Numbers The real numbers are governed by a collection of rules that have to do with addition, multiplication, and inequalities. Rules of addition. • (x + y) + z = x + (y + z) (Law of associativity) • x + y = y + x (Law of commutativity) • x + 0 = x (Law of identity) • x + x = 0 (Law of inverses) Rules of multiplication. • (xy)z = x(yz) (Law of associativity) • xy = yx (Law of commutativity) • x1 = x (Law of identity) • If x ⇤ = 0 then 1 x x = 1 (Law of inverses) Distributive Law. There is a rule that combines addition and multiplication: the distributive law. Of all the rules listed so far, it's arguably the most important. • x(y + z) = xy + xz (Distributive Law) 4 Rules for Numbers The real numbers are governed by a collection of rules that have to do with addition, multiplication, and inequalities. In the rules below, x, y, z C JR. (In other words, .x, y, and z are real numbers.) Rules of addition. • (x + y) + z = x + (y + z) (Law of associativity) • x + y = y + x (Law of commutativity) • .x + 0 = x (Law of identity) • —x + i = 0 (Law of inverses) Rules of multiplication. • (xy)z = …
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