Question 1163627: Classify what subsets -4 belong to. (Natural, Whole, Integers, Rational)
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Natural numbers are variously defined as the positive Integers or the non-negative Integers (does not include zero or does include zero, respectively) depending on the mathematician you talk to and their particular branch of mathematics, but I have never seen a definition of natural numbers that included the negative Integers.
Whole numbers are variously defined as either definition of the Natural Numbers or as all integer, including the negatives.
The Integers include the element 0, the positive Natural Numbers namely, {1, 2, 3,...} and the additive inverses of the positive Naturals, namely {...,-3,-2,-1}, in toto: {...,-3,-2,-1,0,1,2,3}
The Integers are a subset of the Rationals because every integer can be expressed as the quotient of itself and one.
The bottom line is that I cannot completely answer your question until you tell me the precise definition of "Whole Number" upon which the answer to this question should be based.
While you are talking to your instructor about that, you might suggest that your instructor drop all references to Natural and Whole numbers because of the ambiguities such language introduces. Using Integers, Positive Integers, Non-negative Integers (if you want to include zero), Negative Integers, or even Negative integers and Zero (Non-positive is a bit awkward), covers most any situation that you will encounter from where you are in your mathematics learning process through most undergraduate mathematics courses -- and eliminates any ambiguity.
John
My calculator said it, I believe it, that settles it
Answer by ikleyn(52756)  (Show Source):
|
|
|
