Numbers taxonomy

Question 1

Numbers: 3 main types

Answer 1

1. Real numbers
2. Imaginary numbers
3. Complex numbers

Question 2

Numbers: Imaginary numbers

Answer 2

Imaginary numbers are numbers that
contain the number i =√-1

Question 3

Numbers: Complex numbers

Answer 3

Complex numbers are numbers that are expressed as:
a + ib
where a, b are real numbers (b ≠ 0 but a can be equal to zero)

Complex number = Real number + Imaginary number

Question 4

Numbers: Taxonomy map
(within Real numbers)

Answer 4

R = Real
Q = Rational
Z = Integers
W = Whole
N = Natural

Question 5

Numbers: Real numbers (R)

Answer 5

Real numbers are all numbers on the number line, so they can be integers or have decimals even if we have to use infinitely many decimal places.

Question 6

Numbers: Rational numbers (Q)

Answer 6

Real numbers are subdivided into Rational and Irrational.

Rational (from the word: ratio) numbers (denoted as Q which stands for quotient) are numbers formed by dividing one integer by another non-zero integer.

In rational numbers, the decimal expansion either terminates or ends with a repeating sequence:
1/2 = 0.5 (terminates)
2/3 = 0.66666… (repeating sequence)
1/11 = 0.09090909…. (repeating sequence)

Question 7

Numbers: Irrational numbers

Answer 7

• Irrational numbers are numbers that cannot be written as a ratio of two integers.
• In irrational numbers, the decimal expansion neither terminates nor ends with a repeating sequence: π, √2, etc.

Question 8

Numbers: Integers (Z)

Answer 8

Integers are a subset of Rational numbers.

Integers are rational numbers that have no fractional part, they can be positive, negative or zero.

Z = {……-8,-7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,……}

Zero is neither positive nor negative.

Question 9

Numbers: Whole numbers (W)

Answer 9

Whole numbers (subset of Integers which are subset of Rational numbers) are all positive integers AND zero:

W = {0,1,2,3…}

Question 10

Numbers: Natural (counting) numbers (N)

Answer 10

Natural numbers are all positive integers, excluding zero:
1,2,3…

N = {1,2,3,4,5,…}

Natural numbers are also called counting numbers.