Question 1: The integers (from the Latin integer, literally "untouched," hence "whole": the word entire comes from the same origin, but via French) are formed by the natural numbers (including 0) (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (−1, −2, −3, ...). Viewed as a subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {..., −2, −1, 0, 1, 2, ...}. Any number that is NOT an element of this set is NOT an integer. For example, 21, 4, and −2048 are integers; 9.75, 5½, and √2 are not integers.
Question 2: It depends on how you define "Whole Number", and there are three different ways:
1. The set of whole numbers is exactly equivalent to the set of natural numbers, using the definition of natural number to mean the set of positive integers.
2. The set of whole numbers is equivalent to the set of natural numbers, using the definition of natural number to mean the set of non-negative integers.
Note: Case 1 does NOT include zero; case 2 DOES include zero. This is because zero is neither positive nor negative.
3. The set of whole numbers is equivalent to the set of integers.
In cases 1 and 2, the whole numbers do not include the negative numbers, hence -12 is not included in the set because it is a negative number. In case 3, -12 is a whole number.
Tell your teacher that using ambiguous terms such as "whole numbers" and "natural numbers" leads to confusion because of a proliferation of ambiguous definitions. Rather, s/he should use the unambiguously defined sets of integers, positive integers, and non-negative integers.
Question 3: Learn to count. Any number that comes before another number when you are counting is less than the other number; if it comes after, it is greater. Numbers are equal if they are the same or equivalent representations of the same number.
John
My calculator said it, I believe it, that settles it
