To determine the type of number that [tex]\( 4 \)[/tex] is, let's analyze it from different perspectives of number classifications in mathematics:
1. Integer:
- An integer is any whole number, positive or negative, including zero.
- Examples: [tex]\(..., -3, -2, -1, 0, 1, 2, 3, ...\)[/tex]
- Since [tex]\( 4 \)[/tex] is a whole number and does not have any fractional or decimal part, it is considered an integer.
2. Rational Number:
- A rational number is any number that can be expressed as the quotient or fraction [tex]\(\frac{p}{q}\)[/tex] where [tex]\( p \)[/tex] and [tex]\( q \)[/tex] are integers, and [tex]\( q \neq 0 \)[/tex].
- For example, [tex]\( \frac{4}{1} = 4 \)[/tex], which shows that [tex]\( 4 \)[/tex] can be expressed as a fraction of two integers.
- Hence, [tex]\( 4 \)[/tex] is a rational number.
3. Real Number:
- A real number includes all the numbers on the number line, encompassing both rational and irrational numbers (numbers that cannot be expressed as fractions, such as [tex]\( \pi \)[/tex] and [tex]\(\sqrt{2} \)[/tex]).
- Since [tex]\( 4 \)[/tex] is a rational number and therefore a number that can be located on the number line, [tex]\( 4 \)[/tex] is also a real number.
4. Complex Number:
- A complex number can be written in the form [tex]\( a + bi \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are real numbers, and [tex]\( i \)[/tex] is the imaginary unit (where [tex]\( i^2 = -1 \)[/tex]).
- Any real number [tex]\( a \)[/tex] can be thought of as a complex number with [tex]\( b = 0 \)[/tex]. For example, [tex]\( 4 \)[/tex] can be written as [tex]\( 4 + 0i \)[/tex].
- Therefore, [tex]\( 4 \)[/tex] is also considered a complex number.
Based on these classifications, we determine that [tex]\( 4 \)[/tex] is an integer, a rational number, a real number, and a complex number.
