Learning objective
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.
Read the explanation, check the common trap, then practise with flashcards and questions.
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Topic
Number systems
Subtopic
Ordinal numbers
Study support
Understand this objective
Quick explanation
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
- This point belongs to Number systems, especially Ordinal numbers.
- You need to be able to 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.
- 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 Ordinal numbers to exam-style questions, flashcards, and revision notes for Number systems.
Quick student answer
The objects in the ordered set S = {"red", "blue", "green", "yellow"} are written from left to right. What is the ordinal position of "green"?
Direct answer
The ordinal position of "green" is 3rd.
Key terms
- Ordinal number: A number that describes the numerical position of an object in an ordered arrangement.
- Well-ordered set: A set whose objects have been placed in a definite order, allowing their positions to be described using ordinal numbers.
Common trap
Swapping adjacent positions: Read the set from the beginning and count each object carefully, assigning positions in sequence: 1st, 2nd, 3rd, 4th.
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
- 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
