Determine which categories of the following numbers belong a number may be in more than one category

Question

The categories are
neutral
Whole
Integer
Rational
Irrational
The numbers are
Zero
Two
-2
7 over-11
Checkmark thing and three

Answer 1

Let’s categorize the provided numbers based on the definitions of the categories:

1. Neutral: Typically refers to zero.
2. Whole: Non-negative integers (0, 1, 2, 3, ...).
3. Integer: All whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3, ...).
4. Rational: Numbers that can be expressed as a fraction of two integers (where the denominator is not zero).
5. Irrational: Numbers that cannot be expressed as a fraction of two integers.

Now let's categorize each number one by one:

1. Zero (0):

   • Neutral: Yes
   • Whole: Yes
   • Integer: Yes
   • Rational: Yes (0 can be written as 0/1 or any fraction with 0 as the numerator)
   • Irrational: No

2. Two (2):

   • Neutral: No
   • Whole: Yes
   • Integer: Yes
   • Rational: Yes (2 can be written as 2/1)
   • Irrational: No

3. -2:

   • Neutral: No
   • Whole: No
   • Integer: Yes
   • Rational: Yes (-2 can be written as -2/1)
   • Irrational: No

4. 7 over 11 (7/11):

   • Neutral: No
   • Whole: No
   • Integer: No
   • Rational: Yes (it is a fraction of two integers)
   • Irrational: No

5. Checkmark thing (√3, assuming it's meant to represent "the square root of 3"):

   • Neutral: No
   • Whole: No
   • Integer: No
   • Rational: No (it cannot be expressed as a fraction of two integers)
   • Irrational: Yes (√3 cannot be expressed as a precise fraction)

6. Three (3):

   • Neutral: No
   • Whole: Yes
   • Integer: Yes
   • Rational: Yes (3 can be written as 3/1)
   • Irrational: No

Summary of Categories:

• Zero (0): Neutral, Whole, Integer, Rational
• Two (2): Whole, Integer, Rational
• -2: Integer, Rational
• 7 over 11 (7/11): Rational
• Checkmark thing (√3): Irrational
• Three (3): Whole, Integer, Rational

Final Categorized Numbers:

1. Zero: Neutral, Whole, Integer, Rational
2. Two: Whole, Integer, Rational
3. -2: Integer, Rational
4. 7/11: Rational
5. Checkmark thing (√3): Irrational
6. Three: Whole, Integer, Rational