Question
Question What is the cardinal number of the set of positive integers less than 15 ?
Ask by Byrd Bowers. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The set of positive integers less than 15 has 14 elements.
Solution
1. Let the set be \(S = \{x \in \mathbb{N} : x < 15\}\).
2. Since \(S\) contains all positive integers less than 15, the elements of \(S\) are
\[
\{1, 2, 3, \dots, 14\}
\]
3. The number of elements in \(S\) is 14.
4. Thus, the cardinal number of the set is \(\boxed{14}\).
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Simplify this solution Beyond the Answer
The set of positive integers less than 15 includes the numbers 1 through 14, which gives us 14 distinct elements. Therefore, the cardinal number, or the number of elements in this set, is 14. It's like counting your friends at a party – 14 awesome guests ready to have a good time! If you think of positive integers as members of a club, when you set the maximum age limit to 15, only those under that age limit get to join. Thus, all the integers from 1 to 14 are the lively members of this exclusive club, making the cardinality of your club a fun 14!
