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Identify Finite and Infinite Integer Sets

In this activity, students will appreciate the infinite nature of various sets of integers and the finite nature of other subgroups.

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'Identify Finite and Infinite Integer Sets' worksheet

Key stage:  KS 2

Year:  Year 5 11+ worksheets

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Special Numbers

Difficulty level:  

Worksheet Overview

Infinite sets:  a series of numbers that never ends.


The natural numbers are just the numbers starting from 1.

They are 1, 2, 3, 4, 5, ... etc.

We say this set of numbers is infinite because the list will go on forever and will never stop. We can always add one to the 'end' number. 


The whole numbers are the counting numbers and zero.

They are  0, 1, 2, 3, 4, ... etc.

This set of numbers is also infinite.


The integers are natural numbers, the negative numbers and zero.

They are ... -4, -3, -2, -1, 0, 1, 2, 3, 4, ... etc.

This set goes on forever at both 'ends' – at the start and the finish. 

This set is infinite..


Multiples of 3:

3, 6, 9, 12, 15, ... etc.

This also goes on forever because we can always add 3 to the last number.

This set is infinite.



Finite sets: a set of numbers that doesn't go on forever.


The factors of 12:

They are 1, 2, 3, 4, 6 and 12.

There are no more.

This set is finite as it does not go on forever. It has an end.


The multiples of 12 less than 50.

They are 12, 24, 36, and 48.

There are no more, because we cannot go past 50.

This set is finite as it does not go on forever.


That's a lot of names and numbers to remember! You can see this page at any point during the activity by clicking on the red help button on the screen.


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