The meaning of “integer” and “whole number” varies, causing confusion. Integers are natural numbers, including negative and zero. Some only consider positive numbers as integers. It’s better to use specific terms like “positive integers” and “non-negative integers” to avoid confusion.
The difference between an integer and an integer, unfortunately, depends a lot on who is talking about the numbers in question. This is because there is great disagreement about what this type of number represents, which has led to confusion and frustration among math students. Integers are easier to understand, however, since the set of integers simply refers to all natural numbers, including negative, positive, and zero. These numbers are often said to refer only to the positive natural numbers, although sometimes zero is included, and some people use the term “integer” as a synonym for “whole”.
Understanding the difference between an integer and an integer can be difficult, as it depends on how a person uses the term “integer”. It may be easier to start by establishing what integers are, since there is an agreed-upon definition for “integer”. Integers are natural numbers, including negative, zero, and positive numbers. These are natural numbers only and do not include fractions, decimals, irrational numbers, imaginary numbers, or anything else that cannot be expressed as a simple natural number.
With reference to these integers, however, integers can be much more complicated. Many people only consider positive integers, also called count numbers, to be integers, in which case zero would not be an integer. Others treat these numbers as non-negative integers, which would include all positive integers, but would include zero since it’s not a negative number. To further contribute to this confusion, there are also people who use the terms “integer” and “integer” interchangeably, meaning that in such usage there would be no difference between the two terms.
This is why the term is not used frequently in higher level mathematics courses and discussions, as it can be interpreted by different people to mean different things. It is often better to use the terms “integers”, “negative integers”, “positive integers” and “non-negative integers”. Integer would then refer to all natural numbers, including negative, zero, and positive; while negative integer would refer only to negative natural numbers, excluding zero since it is not negative. A positive integer can be used to refer to any positive natural number, although this would exclude zero as it is not positive; while non-negative integers would all be positive natural numbers and zero, since it is not negative.
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