Real Number System Flashcards
What are the two types of numbers?
Rational and irrational
What did the idea of counting begin with?
Began with the number one
How many years ago did prehistoric civilisations count in ones by carving lines on bones?
20,000 years ago
What ancient artefact is known as an example of carving lines on bones? When is the worlds greatest mathematical treasures
Ishango bone
Where was this bone found?
Find in the Democratic Republic of Congo
What do some mathematicians believe the Ishango bone wise?
The oldest artefact containing prime numbers
When was the set of natural numbers developed?
4000 BC in Mesopotamia, Southern Iraq
When was the idea of numbers zero emerged?
In 650 A.D.
Where was the number zero originated from?
Indian mathematics
What did the Indians use zero a placeholder as?
To distinguish numbers such as three and 30
Who was the 1st to use zero in arithmetic operations?
Indian mathematician, Brahmagupta
How was the set of whole numbers invented?
Zero was added to natural numbers
When did the idea of a negative number start emerging?
Long before zero was accepted as a number
In 200 BC what were the Chinese people doing?
Using counting rods in their commercial calculations
What did red rods represent?
Representing positive numbers
What did black rods represent?
Negative numbers
In India what was the negative numbers used for?
To show debts or money owned
In which century did the whole number system extend to include negative numbers?
19th-century
What is integers represented by?
Z
What does the symbol for integers stand for?
Zahlen - German word for numbers
What did integers include?
Phone numbers and negative natural numbers
Why were fractions invented?
To make sense of dividing a hole into equal parts
What set of numbers were invented to include fractions and integers?
Rational numbers
Define rational number
Any number that can be written as one integer divided by another non-zero integer
What is the symbol for rational number?
Q
What is the symbol for rational number stand for?
Quotient since fractions are a form of division
Where and who with decimal fractions developed by?
Chinese in the fourth century
The way we write a news decimals today is based on the work of who?
Scottish mathematician John Napier, 17th century
We are decimal fractions rational or irrational?
Rational is and they can be written as a fraction
What are the two types of decimal fractions?
Terminating decimals and recurring decimals
What is a terminating decimal?
A decimal that has a last digit and it ends
What is a recurring decimal?
A decimal that does not have a last digit and repeats it self
What represents a recurring decimal?
Dot or bar notation
What did Pythagoras believe?
All numbers were rational.
What did Hippasus believe?
Discovered new types of numbers which were irrational numbers
Define irrational number
Any number that cannot be written as one integer divided by another non-zero integer
What are irrational numbers symbol?
Q’
What can irrational numbers be represented by?
On a number line
What are the three most common irrational numbers?
- Square root of numbers that are not perfect squares
- Keep root of numbers that are not perfect cubes
- Pi
What are real numbers?
Numbers that include natural numbers, whole numbers, images, rational numbers and irrational numbers
What is the symbol of real numbers?
R
Are rational numbers true for addition?
True
Are rational numbers true for subtraction?
False
Are rational numbers true for multiplication?
True
Are rational numbers true for division?
False
Are irrational numbers true for addition?
True
Are irrational numbers true for subtraction?
False
Are irrational numbers true for multiplication?
True
Are irrational numbers true for division?
False
