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Algebra 2: Basic Properties of Real Numbers
For Chapter 1; Lesson 1: The Basic Properties of Real Numbers
11
Mathematics
11th Grade
08/21/2012
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Term
x+y is a unique element in R.
 Definition
Closure (+)
Term
(x+y)+ z = x +(y+z)
 Definition
Associative (+)
Term
x+y = y+x
 Definition
Commutative (+)
Term
0 is the additive identity; that is, 0+x = x+0 for all "x" in R, and 0 is the only element in R with this property.
 Definition
Identity (+)
Term
For each x in R, -x is its unique additive inverse; that is, x+(-x) = (-x)+x = 0, and -x is the only element in R relative to x with this property.
 Definition
Inverse (+)
Term
xy is a unique element in R
 Definition
Closure (.)
Term
(xy)z = x(yz)
 Definition
Associative (.)
Term
xy = yx
 Definition
Commutative (.)
Term
1 is the multiplicative identityl that is, for x in R, (1)x = x(1) = x, and 1 is the only element in R with this property.
 Definition
Identity (.)
Term
For each x in R, x ≠ 0, 1/x is its unique multiplicative inverse, that is x(1/x) = 1/x)x = 1, and 1/x is the only element in R relative to x with this property.
 Definition
Inverse (.)
Term
x(y+z) = xy + xz
(x+y)z = xz+xy
 Definition
Distributive
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