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Why are negative integers not considered as natural numbers?

My answer to: Why aren’t negative numbers considered to be natural or whole numbers? (To vote and comment on Quora, visit the link here.)

Natural numbers are the counting numbers. The most elementary/physical form of numbers is the one which is used to count, and they are named “natural numbers”, rightly so. These numbers come naturally to you, e.g. you can either see one chicken or two chickens or three chickens, but not a chicken and a half. Even if you actually have two and a quarter of a pizza, it is actually three pieces in terms of counting: the two pizzas, and the one with a quarter size. The “quarter” and “half” and “one-third” are quantifiers to denote realizations which are not as basic as physical observation—you need to be more educated than “natural”/”raw” intelligence to figure out that one of the pizzas is not the full size. Hence 1, 2, 3,… were “natural” but “2.5” and “4.25” (fractions) were not.

As time progressed, we realized that the zero is not a counting number (since you can’t actually count something that’s not there), but is a quantifier nonetheless (it does denote the quantity of nothingness). Hence it is not “natural” but was called a “whole” number.

Negative integers are quantities that are only a different perspective of looking at the natural numbers. For example, if you spend $100 on a small business, and suffer a loss of $150, then you are left with a “deficit of $50” (i.e., if you wish to talk in terms of an actual, physically interpretable, counting number), or from a different perspective, you are left with –50 dollars. Thus you see, if you actually figure out the meaning of –50, you realize that it’s actually a notation for a “deficit of 50”, not “the number –50 per se”. While “50” means “50” in the most elementary interpretation, “–50” does not mean “–50” in the most elementary interpretation. It does not refer to something you can count directly; the negative sign is only a tool to refer to a deficit of a quantity you can count directly.

Therefore, we can’t treat negative numbers as “natural”. They are only a “perspective” of looking at counting numbers differently, not pure counting numbers per se.

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