4.1 When you apply the rule x-1000 to natural numbers smaller than 1000, you will subtract 1000 from positive numbers that are less than 1000. Since natural numbers are all positive integers starting from 1, 2, 3, and so on, when you subtract a number less than 1000 from 1000, you will always get a negative result. For example:
- 1 - 1000 = -999
- 999 - 1000 = -1
Negative numbers are not considered natural numbers, nor are they whole numbers or rational numbers. They fall under the category of integers, which include all whole numbers, both positive and negative, as well as zero. Therefore, the output numbers obtained by applying the rule x-1000 to natural numbers smaller than 1000 are integers.
Answer for 4.1: Integers
4.2 When you apply the rule +10 to natural numbers smaller than 10, you will add 10 to each of these numbers. Since the smallest natural number is 1 and natural numbers increase by increments of 1, the largest number smaller than 10 is 9. Adding 10 to each number from 1 to 9 will give you the following results:
- 1 + 10 = 11
- 2 + 10 = 12
- ...
- 9 + 10 = 19
All of these resulting numbers are positive integers without fractions or decimals, which indicates they are still natural numbers. Additionally, they are also whole numbers, integers, and rational numbers.
However, since natural numbers best describe positive integers without fractions or decimals, and all of the output numbers fit this description, we categorize them as natural numbers.
Answer for 4.2: Natural numbers
