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 $3.75,2{\displaystyle \frac{1}{2}},\sqrt{2}$ 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. $\sqrt{3}$ ).