The word comes from the Latin language (which isn't a language we use today) which means whole. So this must indicate that an integer is a whole number. If it is a whole number, then it is not a fraction or a decimal.
A whole number is any number including zero and any number that is greater than zero and does not have any fractional part.
[ 0, 1, 2, 3, ...]
Counting numbers are just like the whole number but these numbers don't include the zero. It would be just like you are counting 1, 2, 3, and so on.
[ 1, 2, 3, ...]
The integers are whole numbers, but they include positive and negative numbers as well as the zero.
[ ..., -3, -2, -1, 0, 1, 2, 3, ... ]
My students have been having problems with integers. We have tried temperatures, sea level, checkbook and now the red and yellow counters to help explain the ins and outs of integers. I am looking for more ideas to help explain this concept.