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It's Pre-Algebra, Algebra 1, and Algebra 2.
Terms in this set (15)
Natural or Counting Numbers
1,2,3,4
Whole numbers
0,1,2,3
Odd Numbers
Whole numbers not divisible by 2: 1,3,5,7
Even Numbers
Whole numbers divisible by 2: 0, 2, 4, 6
Negative Integers
-3,-2,-1
Positive Integers
The Natural Numbers: 1,2,3,4
Rational Numbers
Fractions, such as 3/5 or 7/8. All intergers ar rational numbers; for ex. the number 5 may be written as 5/1. All rational numbers can be written as fractions a/b, with a being an integer and b being a natural number. Both terminating decimals (such as .5) and repeating decimals (such as .333) are also rational numbers because they can be written as fractions in this form.
Irrational Numbers
Numbers that cannot be written as fractions a/b, with a being an integer and b being a natural number. √3 and (pi) are examples of irrational numbers.
Axioms of Addition Closure
Closure is when all answers fall into the original set. If you add two even numbers, the answer is still an even number (2 + 4 =6); therefore, the set of even numbers is closed under addition (has closure). If you add two odd numbers, the answer is not an odd numver (3+5=8); therefore, the set of odd numbers is not closed under addtion (no closure).
Axioms of Addition Commutative
means that the order does not made any difference
2+1=1+2
a+b=b+a
Note: commutative does not hold for subtraction
3-2 ≓ 2-3
Axioms of Addition Associative
Means that the grouping does not make any difference.
(2+3) +4 = 2 + (3+4)
(a+b) +c = a +(b+c)
Note: Associative does not hold for subtraction.
4-(2-1) ≓ (4-2) -1
Identity Element of Addition
0
5 +0=0
The Additive Inverse
Is the opposite (negative) of the number? Any number plus its additive inverse equals 0 (the identity).
Axioms of Multiplication Closure
When all answers fall into the original set. If you multiply two even numbers, the answer is still an even number (2 x 4=8); therefore, the set of even numbers is closed under multiplication (has closure). If you multiply two odd numbers, the answer is an odd number (3 x 5 = 15); therefore, the set of odd numbers is closed under multiplication (has closure).
Axioms of Multiplication Commutative
Means that the order does not make any difference.
4x3=3x4
axb=bxa
Note: commutative does not hold for division.
12 / 4 ≠ 4 / 12
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