Question

Which is the largest negative integer?

Answer 1

Hint: An integer (from the Latin integer meaning "whole")  is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, and $\sqrt{2}$ are not. 

Let's consider two positive numbers $5$ and $6$. We can  clearly say $5$ less than $6$.

Similarly consider $-5$ and $-6$. Here $-5$ is greater than $-6$ as these are negative numbers.

Using this logic of comparing numbers, we will find the required answer.

Complete step-by-step answer:
The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, ...), (also called whole numbers or counting numbers), and their additive inverses (the negative integers, i.e., −1, −2, −3, ...).
Now, let us see what a negative integer is.
The negative integers are real integers that are less than 0. For example, −147 and −4 are negative integers, but −0.4181554... and 10 are not (the former is a negative number but not an integer, the latter is a positive integer).
Negative numbers represents the additive inverse of positive numbers.

This can be observed in the below number line image. 

As we move towards right side the value increases throughout the number line.  

Now, we will find the largest negative integer.
If we observe, $-1$ is the last negative number when moving to the right side. So, $-1$ is the largest of all the negative numbers.
Therefore, In conclusion we can say that $-1$ is the largest negative number.

Note: It is also very important to note that one may think that just like the positive integers, the greatest negative integer will be tending to the negative of infinity. But that is not true. Negative of infinity will be the smallest number though its absolute value is the greatest.

When it comes to largest positive number, we can't define. That number will be $\mathrm{\infty }$. And $+1$ is the smallest positive integer.