What is th smallest negative interger?

Answer 1

-1

Answer 2

There are two ways to define the concepts of positive and negative.

One way is to call the integers 0, 1, 2, 3, 4, 5, 6... as positive. In that case, each positive integer will have an additive inverse (a number which, when added to it, will total zero); the list of the additive inverse will be called negative integers:

0, -1, -2, -3, -4, -5, -6...

Using this definition, 0 is both a positive integer and a negative integer.

Mathematicians usually call these sets
non-negative integers (0, 1, 2, 3...) and
non-positive integers (0, -1, -2, -3...).

We use the term "strictly" positive to exclude zero.
Strictly negative integers begin at -1 and go down.

If you are looking at the magnitude of a number (its distance from 0) then 0 is the smallest integer (positive or negative); if you don't lump 0 with negative integers, then -1 has the smallest magnitude.

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However, in math, smaller means going towards the negative.
-60 is smaller than -59. In that way, there is no smaller integer because integers are boundless in both directions. If there were such a thing as a smallest integer, then that would mean that there is such a thing as a biggest integer.
There is not.

Because integers are closed under multiplication (meaning that if you multiply two integers, the result will be an integer), then whatever number you propose as the smallest, I'll simply multiply it by 2 to get an even smaller integer (smaller: twice as far below 0).

Answer 3

-1

Answer 4

-1 unless you make an imaginary number.