Question 1
Learning objective
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'.
Read the explanation, check the common trap, then practise with flashcards and questions.
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Topic
Number systems
Subtopic
Real numbers
Aqa A Level Computer ScienceFundamentals of data representation
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Quick explanation
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'
- This point belongs to Number systems, especially Real numbers.
- You need to be able to 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'.
- 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 Real numbers to exam-style questions, flashcards, and revision notes for Number systems.
Quick student answer
Which set is represented by ℝ?
Direct answer
The set of all real numbers, including natural, rational and irrational numbers
Key terms
- Real number: A number belonging to ℝ, the set that includes natural, rational and irrational numbers and represents possible real-world quantities.
- Irrational number: A real number that is not rational.
Common trap
Treating rational and real as separate categories: Rational numbers are a subset of the real numbers. A rational number is therefore also real; irrational numbers are real but not rational.
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Related learning 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, … }
Natural numbers
- 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
- 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