Closure Property for Integers

Last updated at April 16, 2024 by

For integers

Integers are both positive & negative numbers & zero

 … −3, −2, −1, 0, 1, 2, 3,…..

Operation   Closed or not
Addition 3 + 5 = 8
8 is an integer

Also,
–1 + 0 = –1
–1 is an integer

So, integers are closed under addition 		So, if we add any two numbers,
we get an integer

So, it is closed
Subtraction 3 – 5 = –2
–2 is an integer

Also,
–1 – 0 = –1
–1 is an integer

So, integers are closed under subtraction 		So, if we subtract any two numbers,
we get an integer

So, it is closed
Multiplication 3 × 5 = 15
15 is an integer

Also,
–1 × 0 = 0
0 is an integer

So, integers are closed under multiplication 		So, if we multiply any two numbers,
we get an integer

So, it is closed
Division 3 ÷ 5 = 3/5
But, 3/5 is not an integer

So, integers are not closed under division 		So, if we divide any two numbers,
we do not get an integer

So, it is not closed

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo