Data Representation - Number Sets

What is the symbol for the natural number set?

ℕ

What is the symbol for the integer number set?

ℤ

What is the symbol for the rational number set?

ℚ

What is the symbol for the real number set?

ℝ

What numbers does the integer number set contain?

All whole numbers (both positive and negative)

Why is the integer number set a subset of the rational number set?

As all integers can be written in the form m/1

e.g. 8 can be written in the form 8/1

What does the rational number set contain?

All numbers that can be presented in the form m/n where m and n are integers and n ≠ 0

What does the natural number set contain?

All Positive Integers (Possibly including 0)

What does the irrational number set contain?

All numbers that the rules for rationality do not apply to e.g. π

What does the real number set contain?

All numbers, positive or negative, with or without a fractional part

What is the ordinal number set used for?

To describe the numerical position of an element in a list e.g. 1st is an ordinal number

Which set of numbers do we use for counting and why?

Natural numbers as real world objects don't have fractions or negatives (we only need positive integers).

Which set of numbers do we use for measurement and why?

Real numbers as the measurement may be positive or negative, rational or irrational and real numbers can use an infinite number of decimal places allowing them to represent a number to any level of accuracy.

Which number sets are subsets of the real number set?

The natural, integer, rational and irrational number sets

What do rational decimals do that irrational decimals don't?

Terminate or recur

What should programmers consider when they use irrational numbers?

How accurately to portray them as, the more digits are used, the more data is used.