# Finite or Infinite - Integer Sets

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

Key stage:  KS 2

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Factors and Multiples

Difficulty level:

### QUESTION 1 of 10

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.

Look at 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.

Look at the multiples of 4.

4, 8, 12, 16, 20, ... etc.

Is this set infinite or finite?

infinite

finite

Think about the counting numbers.

Is this set infinite or finite?

infinite

finite

Think about the natural numbers less than 10.

Is this set infinite or finite?

infinite

finite

Think about the whole numbers.

Is this set infinite or finite?

infinite

finite

Think about the 2-digit whole numbers.

Is this set infinite or finite?

infinite

finite

Think about the integers.

Is this set infinite or finite?

infinite

finite

Think about the integers less than 10.

Is this set infinite or finite?

infinite

finite

Think about the even numbers.

Is this set infinite or finite?

infinite

finite

Think about the odd numbers.

Is this set infinite or finite?

infinite

finite

Think about the factors of 10.

Is this set infinite or finite?

infinite

finite

• Question 1

Look at the multiples of 4.

4, 8, 12, 16, 20, ... etc.

Is this set infinite or finite?

CORRECT ANSWER
infinite
EDDIE SAYS
Do times tables ever end? Multiples of a number are the numbers in the times tables and these don\'t end. This means this set is INFINITE.
• Question 2

Think about the counting numbers.

Is this set infinite or finite?

CORRECT ANSWER
infinite
EDDIE SAYS
The counting numbers are 1,2,3,4... etc. This set of numbers never ends so the set is INFINITE.
• Question 3

Think about the natural numbers less than 10.

Is this set infinite or finite?

CORRECT ANSWER
finite
EDDIE SAYS
The natural numbers are just the numbers from 1 onwards. As we are looking for natural numbers less than 10 this means we are looking only at 1,2,3,4,5,6,7,8 and 9. This means that this set is FINITE.
• Question 4

Think about the whole numbers.

Is this set infinite or finite?

CORRECT ANSWER
infinite
EDDIE SAYS
The natural numbers are just the numbers from 0 onwards. This means we are looking at the numbers 0,1,2,3,4,5,6..... etc. This means that this set is INFINITE.
• Question 5

Think about the 2-digit whole numbers.

Is this set infinite or finite?

CORRECT ANSWER
finite
EDDIE SAYS
The smallest 2 digit number is 10, the largest is 99. As we have a smallest and a largest possible number, this set is FINITE.
• Question 6

Think about the integers.

Is this set infinite or finite?

CORRECT ANSWER
infinite
EDDIE SAYS
The integers are just the whole numbers (including positives, negatives and zero). There is no start or end for this so we say this set is INFINITE.
• Question 7

Think about the integers less than 10.

Is this set infinite or finite?

CORRECT ANSWER
infinite
EDDIE SAYS
A bit of a tricky one here. The integers are the whole numbers including positives, negatives and zero. The integers less than 10 has an end point, but doesn\'t have a starting point, we can count back forever. This means the set is INFINITE.
• Question 8

Think about the even numbers.

Is this set infinite or finite?

CORRECT ANSWER
infinite
EDDIE SAYS
The even numbers are the numbers in the 2 times tables. We know that times tables go on forever, so we say this set is INFINITE.
• Question 9

Think about the odd numbers.

Is this set infinite or finite?

CORRECT ANSWER
infinite
EDDIE SAYS
We know that the even numbers go on forever, this means the odd ones do to because for every even number, adding one gives me an odd number. This means this set is INFINITE.
• Question 10

Think about the factors of 10.

Is this set infinite or finite?

CORRECT ANSWER
finite
EDDIE SAYS
The only numbers we can divide 10 by are 1,2,5 and 10. Because this list doesn\'t go on forever, this means the set is FINITE.
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