Algebra II: Unit 1 - Lesson 1 - Real Numbers and Their Subsets

rational

Identify the number as rational or irrational. 0.333...

rational

Identify the number as rational or irrational. 5

irrational

Identify the number as rational or irrational. π

irrational

Identify the number as rational or irrational. √2

real numbers rational numbers

Identify the set described as natural numbers , rational numbers, irrational numbers, real numbers, or integers. It is closed under addition and subtraction, multiplication, and division, with the exception of division by 0 which is not defined.

natural numbers

Identify the set described as natural numbers, rational numbers, irrational numbers, real numbers, or integers. It is closed under addition and multiplication but not closed under subtraction or division.

integers

Identify the sets as integers, natural numbers, or whole numbers. {-2, -1, 0, 1, 2}

whole numbers integers

Identify the sets as integers, natural numbers, or whole numbers. {0, 5, 10, 15}

integers whole numbers natural numbers

Identify the sets as integers, natural numbers, or whole numbers. {4, 5, 6, 7}

integers whole numbers

Identify the sets as integers, natural numbers, or whole numbers. {0, 8, 9, 10}

whole numbers

Numbers {0, 1, 2, 3, 4, ...} are called __.

Natural numbers

____ are numbers {1, 2, 3, 4, ...} and designed with ℕ .

Irrational numbers

____ are real numbers which cannot be written as the ratio of two integers; designed will ℚ'.

Closure

____ is the property of an operation and a set that the performance of the operation on members of the set always yields a member of the set.

Rational numbers

_____ are numbers of the form {a/b ∣ a,b ∈ ℤ, b ≠ 0} and designated with ℚ .

Integers

_____ are numbers {0, +1, -1, +2, -2, ...} ℤ.

Real numbers

_____ are the rational numbers together with the irrational numbers; designed with ℝ.

rational numbers

numbers of the form a {a/b | a,b ∉ ℤ, b ≠ 0} 0 and designated with ℚ

integers

numbers {0, +1, −1, +2, −2, . . .} and designated with ℤ

whole numbers

numbers {0, 1, 2, 3, . . .}

natural numbers

numbers {1, 2, 3, 4, . . .} and designated with ℕ

irrational numbers

real numbers which cannot be written as the ratio of two integers; designated with ℚ'

closure

the property of an operation and a set that the performance of the operation on members of the set always yields a member of the set

real numbers

the rational numbers together with the irrational numbers; designated with ℝ