Learning objective
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, … }
Read the explanation, check the common trap, then practise with flashcards and questions.
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Topic
Number systems
Subtopic
Natural numbers
Aqa A Level Computer ScienceFundamentals of data representation
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Quick explanation
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, … }
- This point belongs to Number systems, especially Natural numbers.
- You need to be able to 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, … }.
- Use the linked flashcards and practice questions to check recall, then practise applying the idea in an exam-style answer.
Why it matters
This objective helps connect Natural numbers to exam-style questions, flashcards, and revision notes for Number systems.
Quick student answer
Which set correctly represents the natural numbers as specified?
Direct answer
{0, 1, 2, 3, ...}
Key terms
- Natural number: A number belonging to the set ℕ, which is defined here as {0, 1, 2, 3, …}.
- Set: A collection of values considered together; ℕ is the set containing the natural numbers.
Common trap
Leaving zero out of ℕ: Use the definition in this specification: ℕ = {0, 1, 2, 3, …}, so zero is included.
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Related learning 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, … }
Integer numbers
- 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.
Rational numbers
- 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.
Irrational numbers
- 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'.
Real numbers
- 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.
Ordinal numbers