Question
Describe all the sets and subsets the number −25 belongs to.(1 point)
Answers
GPT-4o mini
The number \(-25\) belongs to several sets and subsets in mathematics. Here are the main categories:
1. **Real Numbers (\(\mathbb{R}\))**: \(-25\) is a real number, so it belongs to the set of all real numbers.
2. **Rational Numbers (\(\mathbb{Q}\))**: \(-25\) is a rational number because it can be expressed as the fraction \(-25/1\).
3. **Integers (\(\mathbb{Z}\))**: \(-25\) is an integer, which means it belongs to the set of all integers, which includes positive and negative whole numbers, as well as zero.
4. **Negative Integers**: \(-25\) is specifically a negative integer, so it belongs to the subset of negative integers.
5. **Whole Numbers**: \(-25\) does not belong to the set of whole numbers since they include only non-negative integers (0, 1, 2, ...).
6. **Natural Numbers**: \(-25\) does not belong to the set of natural numbers as they are the positive integers (1, 2, 3, ...).
In summary, the number \(-25\) belongs to the following sets and subsets:
- Real Numbers \((\mathbb{R})\)
- Rational Numbers \((\mathbb{Q})\)
- Integers \((\mathbb{Z})\)
- Negative Integers (subset of \(\mathbb{Z}\))
1. **Real Numbers (\(\mathbb{R}\))**: \(-25\) is a real number, so it belongs to the set of all real numbers.
2. **Rational Numbers (\(\mathbb{Q}\))**: \(-25\) is a rational number because it can be expressed as the fraction \(-25/1\).
3. **Integers (\(\mathbb{Z}\))**: \(-25\) is an integer, which means it belongs to the set of all integers, which includes positive and negative whole numbers, as well as zero.
4. **Negative Integers**: \(-25\) is specifically a negative integer, so it belongs to the subset of negative integers.
5. **Whole Numbers**: \(-25\) does not belong to the set of whole numbers since they include only non-negative integers (0, 1, 2, ...).
6. **Natural Numbers**: \(-25\) does not belong to the set of natural numbers as they are the positive integers (1, 2, 3, ...).
In summary, the number \(-25\) belongs to the following sets and subsets:
- Real Numbers \((\mathbb{R})\)
- Rational Numbers \((\mathbb{Q})\)
- Integers \((\mathbb{Z})\)
- Negative Integers (subset of \(\mathbb{Z}\))