Real Number System?

Question

It says- Tell whether the following are true or false and explain your answeres:

A. Real Numbers are a subset of Integers.
B. Whole Numbers are a subset of Natural Numbers.
C. Integers are a subset of Real Numbers.

I think B is false, I think Natural Numbers are a subset of Whole Numbers. Am I correct? Help me on ABC, plz. Thank you!:)

Answer 1

The integers are a subset of the reals.

"Whole number" means different things in different books; some authors equate them to the naturals, others to the integers. So check your book to see which definition your author uses.

Answer 2

A) The real numbers contain all integers, rationals and irrational numbers. So things like 1, 4, 0.75 and PI are all real numbers. It would be false to say that the integers contain the real numbers, since any fraction or irrational number is a real number, but is certainly not an integer.

B) The natural numbers are all positive integers, not including zero. You can think of this as the set of numbers you can use to count anything in "nature". There are three rocks, or two trees, or fourteen bushes. Whole numbers are the natural numbers with 0 added into the mix. Technically you can't count "0" of anything in nature, except to say that "There are no rocks here." Thus, whole numbers are NOT a subset of the natural numbers.

C) See my answer for A. Every integer is a rational number, and thus this is true.

Answer 3

A. False. Not every real number is also an integer.

B. False. Zero is a whole number but not a natural number.

C. True. Every integer is also a real number.

Answer 4

1.)The square root of 25 be classified as a: Real Number Rational Number Integer Whole Number Natural Number 2.) 3.5 can be classified as: Real Number Rational Number 3.) pi can be classified as: Real Number Irrational Number 4.) the square root of 5 can be classified as: Real Number Irrational Number

Answer 5

A. False
Integers are part of the reals
B. False
Whole numbers include 0, naturals do not
C. True