Answered

IDNLearn.com: Where questions are met with accurate and insightful answers. Ask your questions and receive accurate, in-depth answers from our knowledgeable community members.

Which of the following sets is not finite?

A. [tex]\(\{x \mid x \text{ is a natural number less than 10}\}\)[/tex]
B. [tex]\(\{x \mid x \text{ is an integer that is less than 0}\}\)[/tex]
C. [tex]\(\{x \mid x \text{ is a whole number between 0 and 10}\}\)[/tex]

Sagot :

GinnyAnsweridn
To determine which of the given sets is not finite, we need to analyze each set individually.

1. First Set: {x | x is a natural number less than 10}
- Natural numbers are the set of positive integers starting from 1.
- Therefore, this set contains: {1, 2, 3, 4, 5, 6, 7, 8, 9}
- There are 9 elements in this set, which is a finite number.

2. Second Set: {x | x is an integer that is less than 0}
- Integers less than 0 are negative integers.
- This set includes all negative integers: {..., -4, -3, -2, -1}
- This set continues indefinitely and has no end.
- Therefore, this set is infinite.

3. Third Set: {x | x is a whole number between 0 and 10}
- Whole numbers are non-negative integers, starting from 0.
- This set includes the numbers: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
- There are 11 elements in this set, which is a finite number.

Upon examining these sets, we find:

- The first set has 9 elements and is finite.
- The second set continues indefinitely with negative integers and is infinite.
- The third set has 11 elements and is finite.

Hence, the set which is not finite is:
O{xlx is an integer that is less than 0}
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.