Every negative integer J is less than or equal to its inverse

Here we have the statement:

" Every negative integer J is less than or equal to its inverse"

First, remember that when we are talking about negative numbers, the ones that are closer to 0 are the larger ones.

For example, if we have -1 and -5

-1 is closer to zero, then:

-1 > -5

Now we have a negative integer J.

The smallest negative integer is -1

it's inverse is 1/-1 = -1

Then, if j = -1:

j = 1/j

-1 = 1/-1 = -1

and if  j < -1 (-2, -3, -4, -5)

then for example, for j = -2

1/-2 = - (1/2)

and (-1/2) is a number between -1 and 0

So it is closer to zero than -2

then:

(-1/2) > -2.

Then, concludin, if IjI > 1, we have always that  0 > 1/j > -1 > j.