Number systems | AQA Computer Science 7517

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Natural numbers1 objectives

Natural numbers: Be familiar with the concept of a natural number and the set ℕ of natural numbers (including zero). ℕ = {0, 1, 2, 3, … }

Integer numbers1 objectives

Integer numbers: Be familiar with the concept of an integer and the set ℤ of integers. ℤ = { …, -3, -2, -1, 0, 1, 2, 3, … }

Rational numbers1 objectives

Rational numbers: Be familiar with the concept of a rational number and the set ℚ of rational numbers, and that this set includes the integers. ℚ is the set of numbers that can be written as fractions (ratios of integers). Since a number such as 7 can be written as 7/1, all integers are rational numbers.

Irrational numbers1 objectives

Irrational numbers: Be familiar with the concept of an irrational number. An irrational number is one that cannot be written as a fraction, for example √2.

Real numbers1 objectives

Real numbers: Be familiar with the concept of a real number and the set ℝ of real numbers, which includes the natural numbers, the rational numbers and the irrational numbers. ℝ is the set of all 'possible real world quantities'.

Ordinal numbers1 objectives

Ordinal numbers: Be familiar with the concept of ordinal numbers and their use to describe the numerical positions of objects. When objects are placed in order, ordinal numbers are used to tell their position. For example, if we have a well-ordered set S = {‘a’, ‘b’, ‘c’, ‘d’}, then ‘a’ is the 1st object, ‘b’ the 2nd, and so on.

Counting and measurement1 objectives

Counting and measurement: Be familiar with the use of: • natural numbers for counting • real numbers for measurement. 64

Natural numberSetIntegerℤRational numberℚIrrational numberFractionReal numberOrdinal numberWell-ordered set

Read the definition carefully: When deciding whether a value is natural, check it against ℕ = {0, 1, 2, 3, …} and remember that zero is included.
Check for whole-number values: When deciding whether a value belongs to ℤ, check that it is a negative whole number, zero, or a positive whole number.

Leaving zero out of ℕ: Use the definition in this specification: ℕ = {0, 1, 2, 3, …}, so zero is included.
Forgetting that zero is an integer: Remember that 0 is explicitly included in the definition of ℤ, even though it is neither positive nor negative.

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