Integer definition Classify the following number: -19.

There is no general agreement as to what constitutes a whole number. All that is sure is that it does not have a fractional part or, if you want to split hairs figuratively speaking, has a fractional part that is 0.
An integer is any one number in the set infinite Z ={.., -15,-14,...,-2,-1, 0,1,2, ..., 14, 15, ...}.

Here are links to MathWorld by Wolfram Research where you can get more authoritative definitions.
http://mathworld.wolfram.com/NaturalNumber.html
http://mathworld.wolfram.com/WholeNumber.html

If you are a student, just ask your teacher or professor. He/She may be of a different opinion.
-19 is an integer.