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Identity Element of Addition

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Mar 1, 2020

Cards (15)

Section 1

(15 cards)

Identity Element of Addition

Front

0 5 +0=0

Back

Odd Numbers

Front

Whole numbers not divisible by 2: 1,3,5,7

Back

Natural or Counting Numbers

Front

1,2,3,4

Back

Negative Integers

Front

-3,-2,-1

Back

Whole numbers

Front

0,1,2,3

Back

The Additive Inverse

Front

Is the opposite (negative) of the number? Any number plus its additive inverse equals 0 (the identity).

Back

Positive Integers

Front

The Natural Numbers: 1,2,3,4

Back

Irrational Numbers

Front

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.

Back

Axioms of Addition Commutative

Front

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

Back

Rational Numbers

Front

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.

Back

Even Numbers

Front

Whole numbers divisible by 2: 0, 2, 4, 6

Back

Axioms of Multiplication Closure

Front

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).

Back

Axioms of Multiplication Commutative

Front

Means that the order does not make any difference. 4x3=3x4 axb=bxa Note: commutative does not hold for division. 12 / 4 ≠ 4 / 12

Back

Axioms of Addition Associative

Front

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

Back

Axioms of Addition Closure

Front

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).

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