Question

Find all the integers between $ -4 $ and 4.

Answer 1

Hint: Integers are the numbers which do not have any decimal part after the decimal point.
Integers can be positive, negative or neutral (0).
There are exactly n integers "from" 1 to n (n is positive), including both 1 and n. The same is true from $ -1 $ to $ -n $ .

Complete step-by-step answer:
Let us divide the integers into three sets: positive, negative and 0.
Note that the integers "between" $ -4 $ and 4, do not include the integers $ -4 $ and 4 themselves.
For the positive integers, there will be 3 integers from 1 to 3.
For the negative integers, there will be 3 integers from $ -1 $ to $ -3 $ .
∴ The total number of integers, including 0, will be:
  $ 3+3+1 $
= 7
These integers can be listed down: $ -3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3 $ .
So, the correct answer is “ $ -3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3 $ ”.

Note: There are $ b-a+1 $ integers from integer a to integer b, including both of them.
An integer (from the Latin "integer" meaning "whole") is defined as a number that can be written without a fractional component. Integers can be positive, negative or neutral (0).
e.g. $ -1,\ 24,\ 0 $ etc. are integers, while $ 3.75,\ 2\dfrac{1}{2},\ \sqrt{2} $ are not.
The numbers which are not integers are either rational (can be expressed as a ratio of two integers.) or irrational (cannot be expressed as a ratio of two integers. e.g. $ \sqrt{3} $ ).