Quandaries
and Queries 

Subject: Subsets of the Real Number System I am trying to help a new African student who speaks more French than English in a monolingual English school here in the United States. My limited French does not include mathematical terms, so I have been looking for resources to help him make the transition to English. In looking for resources to help him, I have stumbled across something I never thought about before. U.S. schools teach the following subsets of the real number system: Whole numbers: {0,1,2,3,4,...} Integers: {...4,3,2,1,1,2,3,4,...} Rationals: All of the above, plus fractions with integral numerators and denominators, terminating and repeating decimals Irrationals: Numbers that cannot be expressed as the ratio of two integers, such as nonrepeating, nonterminating decimals. In looking for a French equivalent of the word "integer", I found that the word seems not to actually exist in French, and that Canadian schools use the term "natural number" to describe what we have been trained to call "whole numbers," while using the term "whole number" to describe what we have been trained to call "integers." Who decided what constitutes each subset, and when? Why is it defined differently in different places? Shouldn't we all agree on common definitions? Christine 

Hi Christine, I think I have heard "Entiers relatifs" used to describe the integers, including the negative numbers. Concerning your comment: "Shouldn't we all agree on common definitions?", well you may have your own ideas on the subject, but the world at large certainely doesn't work like that: Even in english, the same number can have two different names and different numbers can have the same name; see our table of some number words in the answer to a question on billions and more. The phenomenon of seeing two systems coexisting in the same world is not restricted to the names of numbers and sets of numbers: Some people think in miles, pounds and gallons, others in kilometers, grams and liters, some people use Windows environment on their computers, others MacIntosh or Solaris, some people drive on the left side of the road, others on the left, and so on. In all these cases it would perhaps be simpler to have everybody working with the same system, but who is to say that everybody else should switch to their system? Claude 

