Teachers who fail to acknowledge this and who insist (especially to young children) that certain definitions are "wrong" are doing a huge disservice to their students' appreciation of mathematics - it undermines the universality entirely and teaches them that this is just another subject where the teacher pompously thinks they're always right. To me, the important takeaway for mathematical education is the idea that definitions vary by contexts and cultures, and that the underlying mathematical idea is independent of how a particular writer or teacher chooses to present it. But more importantly, they'll take care to define the terms they use in the context they're using them in. (albeit typically using the more rigorous term integers, which is always understood to include negative numbers and zero). Mathematicians writing rigorously and with a concern for not raising annoying pedantic rehashing of this topic will tend to write things out explicitly as "positive whole numbers", "non-negative whole numbers", etc.
WHOLE NUMBERS PROFESSIONAL
There is no agreed-upon rigorous definition of the term, and in fact it's largely viewed by professional mathematicians as a matter of philosophy of mathematics and of one's particular school/ideology whether you consider "whole numbers" to include negatives or even zero. There's absolutely nothing "incorrect" about this.Īnd whole number is rarely used as a precise designation outside of school mathematics I’m more curious about incorrect things in them. I ask because I’m using American textbooks to study maths and now I’m more curious about incorrect things in them. Languages regard 0 as neither positive nor negative.ĭoes anyone know why American textbooks decided to go this way? (“positif” and “négatif”, respectively), as the French think of 0 asīoth positive and negative, whereas English, German, and many other However, be careful with the concepts of positive and negative −1 and down non-positive integers means 0 and down. Itself includes positive, 0, and negative positive integers means 1Īnd up non-negative integers means 0 and up negative integers means The best way to avoidĪmbiguity is to be explicit about which integers you are referring toīy applying the appropriate adjective to “integer”. To the English “entire” in the sense of whole. “nombre entier” (often simply “entier”), with entier being a cognate Which literally means whole numbers, as well as French terminology Terminology where the formal name for integers is “ganze Zahlen”, Certainly −1, −2, … have noįractional part so they are whole. Professional mathematicians (researchers) tend to use the term whole numbers somewhat more informally as a synonym for integers, with No clue as to the origin of this poor usage. In this context negative numbers cannot be whole numbers. I found a Quora answer which mentions:Īccording to American middle and high school textbooks, the set of whole numbers includes all positive integers and 0, and not anythingĮlse. I was suspicious about this answer and I decided to dig more into this.
The whole numbers are also called the positive integers (or the nonnegative integers, if zero is included). Looking up for definition for whole numbers on Google yields a result which mentions:
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