Describe all the sets and subsets the number −34 belongs to.
The number -34 belongs to several sets and subsets:
- The set of integers (Z), which includes all whole numbers and their negatives.
- The set of negative integers, which includes all integers less than zero.
- The set of even integers, since -34 can be divided by 2 evenly.
- The subset of counting numbers, which are positive integers (since -34 is not a positive integer, it would be excluded from this subset).
To determine all the sets and subsets the number -34 belongs to, we need to first understand the various mathematical sets. Here are the commonly used sets and their subsets in relation to -34:
1. Natural Numbers (N): This set includes all positive integers starting from 1. As -34 is not a positive integer, it does not belong to this set.
2. Whole Numbers (W): This set includes all non-negative integers starting from 0. Since -34 is negative, it does not belong to this set either.
3. Integers (Z): This set includes all positive and negative whole numbers, including 0. As -34 is a negative whole number, it belongs to this set.
4. Rational Numbers (Q): This set includes all numbers that can be expressed as fractions (where the numerator and denominator are integers). -34 can be written as -34/1, which is a fraction, so it belongs to this set.
5. Real Numbers (R): This set includes all rational and irrational numbers. Since -34 is a rational number, it belongs to this set.
6. Complex Numbers (C): This set includes all numbers of the form a + bi, where a and b are real numbers, and i is the imaginary unit (√-1). As -34 can be written as -34 + 0i, it belongs to this set.
To summarize, -34 belongs to the sets: Integers (Z), Rational Numbers (Q), Real Numbers (R), and Complex Numbers (C).