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Definition: Numbers that cannot be expressed as a simple fraction. Examples: $\pi$, $e$, $\sqrt{2}$

Definition: The set of all possible numbers on the number line, including rational and irrational numbers. Examples: $-\frac{5}{2}$, $\pi$, 0, 3

Definition: Numbers that give a negative result when squared. Examples: $\sqrt{-1}$, written as 'i'; $3i$, $-2i$

Definition: Numbers consisting of a real and an imaginary part. Examples: $1 + 2i$, $-3 - 4i$, $0 + i$

Definition: Natural numbers greater than 1 that have more than two distinct positive divisors. Examples: 4, 6, 8, 9, 10, ...

Definition: Real or complex numbers that are not algebraic; they do not satisfy any finite polynomial equation with rational coefficients. Examples: $\pi$, $e$

Definition: Numbers that say how many of something there are, such as one, two, three, four, etc. They do not indicate order. Examples: 1 (one), 6 (six), 15 (fifteen)

Definition: Numbers that tell the position of something in a list, such as first, second, third, etc. They indicate an ordered sequence. Examples: 1st (first), 2nd (second), 3rd (third)

Definition: The set of natural numbers including zero. Examples: 0, 1, 2, 3, ...

Definition: The set of positive integers, not including zero. Examples: 1, 2, 3, ...

Definition: The set of whole numbers and their negatives. Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...

Definition: A system of numbers where the value of each digit depends on its position with respect to the most significant digit. They are defined in terms of a prime number p. Examples vary and could involve series representation.

Definition: Natural numbers greater than 1 that have only two distinct positive divisors: 1 and the number itself. Examples: 2, 3, 5, 7, 11, ...

Definition: Numbers that are the root of a non-zero polynomial equation with rational coefficients. Examples: $\sqrt{2}$, $\frac{3}{2}$, $-1$, $\sqrt[3]{5}$