z-axis
In three dimensions, the third axis, at right angles to both the x-axis and the y-axis. It shows depth or height.
z-score
How many standard deviations a value is above or below the mean: z = (value − mean) ÷ standard deviation.
Zeno's paradoxes
Ancient puzzles by Zeno of Elea, such as the claim that you can never reach a wall because you must first go half the distance, then half of what is left, and so on forever. The sum 1/2 + 1/4 + 1/8 + … = 1 shows you do arrive.
Zero
The first whole number. Adding zero to any number leaves the number unchanged (a + 0 = a), so zero is called the additive identity. Any number times zero is zero, and dividing by zero is undefined.
Zero angle
An angle that measures 0°. Its two rays point in exactly the same direction, so they lie on top of each other.
Zero as a placeholder
A zero written in a place-value position to show that the place is empty, as in 405, which has no tens.
Zero exponent
Any nonzero number raised to the power 0 equals 1: x⁰ = 1.
Zero of a function
An input value that makes a function equal 0. On a graph, the zeros are the x-intercepts; they are also called roots.
Zero pair
A positive and a negative of the same amount, such as +1 and −1, that add up to zero. Zero pairs are used with counters and algebra tiles.
Zero product property
If the product of two factors is zero, at least one of the factors is zero: if ab = 0, then a = 0 or b = 0. It is used to solve factored equations.
Zero property of multiplication
Any number multiplied by zero equals zero: a × 0 = 0.
Zero slope
The slope of a horizontal line. Its rise is 0, so the line goes neither up nor down, and its equation is y = b.
Zillion
An informal word for an extremely large number of unspecified size. It is not a real number name like million or billion.