Answered

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Which of the following sets is not finite?

A. [tex]\(\{x \mid x \text{ is an integer that is less than 0}\}\)[/tex]

B. [tex]\(\{x \mid x \text{ is a natural number less than 10}\}\)[/tex]

C. [tex]\(\{x \mid x \text{ is a whole number between 0 and 10}\}\)[/tex]

Sagot :

GinnyAnsweridn
To determine which of the following sets is not finite, let's analyze each given set in detail.

1. Set of integers less than 0:
This set includes all integer numbers that are less than zero. Examples of such numbers are −1, −2, −3, −4, and so on. It's important to observe that there is no upper limit for negative integers; we can always find another integer that is less than the previous one. Therefore, the set of integers less than 0 extends infinitely in the negative direction. Consequently, this set is not finite.

2. Set of natural numbers less than 10:
Natural numbers are the positive integers beginning from 1. Therefore, the natural numbers less than 10 are: 1, 2, 3, 4, 5, 6, 7, 8, and 9. This set is limited to nine specific numbers and does not extend indefinitely. Thus, the set of natural numbers less than 10 is finite.

3. Set of whole numbers between 0 and 10:
Whole numbers are all the non-negative integers, which includes 0. Therefore, the whole numbers between (and including) 0 and 10 are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. This set consists of eleven specific numbers and is clearly bounded. Hence, the set of whole numbers between 0 and 10 is finite.

After analyzing the details of each set, we conclude that:

The set of integers less than 0 is not finite.

So, the final answer to the question is:

3
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