Algebra II Unit 1
Identity
the result is itself; 4+0=4, 4*1=4
Closure Property
A set is ___ (under an operation) if the operation always produces an element of the same set. If an element outside the set is produced, then the operation is not ___.
Z; Ex: ... -3, -2, -1, 0, 1, 2, 3...
Integers
True
Integers are closed under multiplication.
I; Ex: 3.14..., e
Irrational Numbers
False; sq. root of 10- sq. root of 10=0
Irrational numbers are closed under subtraction.
N; Ex: 1, 2, 3...
Natural Numbers
True
Natural numbers are closed under division.
True
Negative numbers are closed under addition.
Rational Number
Numbers in which the deciaml form either terminates or repeats.
Irrational Numbers
Numbers which the decimal form never terminates and does not repeat.
False; 5+3=8
Odd numbers are closed under addition.
False; 13-7=6
Prime numbers are closed under subtraction.
Q; Ex: 1/2, 2 2/3, 10/6, 0, 1, -1
Rational Numbers
R; Ex: all numbers learned so far
Real Numbers
Integers, Whole Numbers, Natural Numbers
Subsets of Rational Numbers
W; Ex: 0, 1, 2, 3...
Whole Numbers
False; 7/6
Whole numbers are closed under division.
Distributive
a(b+c)=ab+ac
Associative
changing ( ); 2+(4+6)=(2+4)+6
Commutative Property
changing order; 2+4=4+2, xy=yx
Inverse
the result is zero for addition and one for multiplication; 4+(-4)=0, 4*1/4=1