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Math > Real Number System > Flashcards

Real Number System Flashcards

1
Q

What are the two types of numbers?

A

Rational and irrational

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2
Q

What did the idea of counting begin with?

A

Began with the number one

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3
Q

How many years ago did prehistoric civilisations count in ones by carving lines on bones?

A

20,000 years ago

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4
Q

What ancient artefact is known as an example of carving lines on bones? When is the worlds greatest mathematical treasures

A

Ishango bone

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5
Q

Where was this bone found?

A

Find in the Democratic Republic of Congo

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6
Q

What do some mathematicians believe the Ishango bone wise?

A

The oldest artefact containing prime numbers

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7
Q

When was the set of natural numbers developed?

A

4000 BC in Mesopotamia, Southern Iraq

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8
Q

When was the idea of numbers zero emerged?

A

In 650 A.D.

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9
Q

Where was the number zero originated from?

A

Indian mathematics

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10
Q

What did the Indians use zero a placeholder as?

A

To distinguish numbers such as three and 30

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11
Q

Who was the 1st to use zero in arithmetic operations?

A

Indian mathematician, Brahmagupta

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12
Q

How was the set of whole numbers invented?

A

Zero was added to natural numbers

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13
Q

When did the idea of a negative number start emerging?

A

Long before zero was accepted as a number

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14
Q

In 200 BC what were the Chinese people doing?

A

Using counting rods in their commercial calculations

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15
Q

What did red rods represent?

A

Representing positive numbers

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16
Q

What did black rods represent?

A

Negative numbers

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17
Q

In India what was the negative numbers used for?

A

To show debts or money owned

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18
Q

In which century did the whole number system extend to include negative numbers?

A

19th-century

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19
Q

What is integers represented by?

A

Z

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20
Q

What does the symbol for integers stand for?

A

Zahlen - German word for numbers

21
Q

What did integers include?

A

Phone numbers and negative natural numbers

22
Q

Why were fractions invented?

A

To make sense of dividing a hole into equal parts

23
Q

What set of numbers were invented to include fractions and integers?

A

Rational numbers

24
Q

Define rational number

A

Any number that can be written as one integer divided by another non-zero integer

25
Q

What is the symbol for rational number?

A

Q

26
Q

What is the symbol for rational number stand for?

A

Quotient since fractions are a form of division

27
Q

Where and who with decimal fractions developed by?

A

Chinese in the fourth century

28
Q

The way we write a news decimals today is based on the work of who?

A

Scottish mathematician John Napier, 17th century

29
Q

We are decimal fractions rational or irrational?

A

Rational is and they can be written as a fraction

30
Q

What are the two types of decimal fractions?

A

Terminating decimals and recurring decimals

31
Q

What is a terminating decimal?

A

A decimal that has a last digit and it ends

32
Q

What is a recurring decimal?

A

A decimal that does not have a last digit and repeats it self

33
Q

What represents a recurring decimal?

A

Dot or bar notation

34
Q

What did Pythagoras believe?

A

All numbers were rational.

35
Q

What did Hippasus believe?

A

Discovered new types of numbers which were irrational numbers

36
Q

Define irrational number

A

Any number that cannot be written as one integer divided by another non-zero integer

37
Q

What are irrational numbers symbol?

A

Q’

38
Q

What can irrational numbers be represented by?

A

On a number line

39
Q

What are the three most common irrational numbers?

A
  1. Square root of numbers that are not perfect squares
  2. Keep root of numbers that are not perfect cubes
  3. Pi
40
Q

What are real numbers?

A

Numbers that include natural numbers, whole numbers, images, rational numbers and irrational numbers

41
Q

What is the symbol of real numbers?

A

R

42
Q

Are rational numbers true for addition?

A

True

43
Q

Are rational numbers true for subtraction?

A

False

44
Q

Are rational numbers true for multiplication?

A

True

45
Q

Are rational numbers true for division?

A

False

46
Q

Are irrational numbers true for addition?

A

True

47
Q

Are irrational numbers true for subtraction?

A

False

48
Q

Are irrational numbers true for multiplication?

A

True

49
Q

Are irrational numbers true for division?

A

False

Math (6 decks)

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