Learning objective
Integer numbers: Be familiar with the concept of an integer and the set ℤ of integers. ℤ = { …, -3, -2, -1, 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
Integer numbers
Study support
Understand this objective
Quick explanation
Integer numbers: Be familiar with the concept of an integer and the set ℤ of integers. ℤ = { …, -3, -2, -1, 0, 1, 2, 3, … }
- This point belongs to Number systems, especially Integer numbers.
- You need to be able to integer numbers: Be familiar with the concept of an integer and the set ℤ of integers. ℤ = { …, -3, -2, -1, 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 Integer numbers to exam-style questions, flashcards, and revision notes for Number systems.
Quick student answer
Which statement best describes an integer?
Direct answer
A whole-number value that may be negative, zero, or positive
Key terms
- Integer: A whole-number value that may be negative, zero, or positive.
- ℤ: The symbol used for the set of integers: { …, -3, -2, -1, 0, 1, 2, 3, … }.
Common trap
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.
Related questions
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Flashcard prompts
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Revision tools
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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
- 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