counting: 1, 2, 3, 4, ...
whole: 0, 1, 2, 3, 4, ...
integers: ... , -3, -2, -1, 0, 1, 2, 3, ...
rational: all numbers that can be written as a ratio of integers
irrational: all numbers that cannot be written as a ratio of integers
real: all the numbers listed above
complex: numbers of the form a + bi, where a and b are real numbers, and i is the imaginary unit (i.e., the square root of -1)
That's correct! Here is a breakdown of each number system:
1. Counting numbers: The counting or natural numbers start from 1 and continue indefinitely without any negative numbers. Examples include 1, 2, 3, 4, and so on.
2. Whole numbers: Whole numbers include all the counting numbers (1, 2, 3, 4, etc.) along with zero (0). Examples include 0, 1, 2, 3, 4, and so on.
3. Integers: Integers include all whole numbers (0, 1, 2, 3, 4, etc.) along with their negative counterparts and zero. Examples include ..., -3, -2, -1, 0, 1, 2, 3, and so on.
4. Rational numbers: Rational numbers are all the numbers that can be expressed as fractions or ratios of integers. They can be written in the form p/q where p and q are integers, and q is not zero. Examples include 1/2, -3/4, 5/8, and so on.
5. Irrational numbers: Irrational numbers are numbers that cannot be expressed as fractions or ratios of integers. They cannot be represented by terminating or repeating decimals. Examples include √2 (square root of 2), π (pi), and e (Euler's number).
6. Real numbers: Real numbers include all the numbers mentioned above: counting numbers, whole numbers, integers, rational numbers, and irrational numbers. They cover every possible number that can be represented on a number line.
I hope this breakdown helps clarify the different number systems for you!