Addition : Addition is the mathematical operation that describes increasing a number by an amount equal to a second number. The mathematical symbol for addition is the plus sign $+.$ The term addition is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.

Zero : The number 0.

Cup : A unit to measure volume. A cup is defined as half a pint. A cup is about 0.24 liters.

Gallon : A gallon is a unit for measuring volume. A gallon is 4 quarts or about 3.8 liters.

Pint : A pint is a unit for measuring volume. 2 pints are a quart, and 2 cups are a pint.

Quart : A quart is a unit for measuring volume. 2 pints are a quart and 4 quarts are a gallon.

Cube root : The cube root of $x$, normally written as $\sqrt[3]{x}$ or as $x^{\frac{1}{3}}$ is the number whose third power equals $x$. In other words it is defined as the solution of the equation $(\sqrt[3]{x})^3=x.$

Fractional exponent : The definition of a power with a fractional exponent is $x^\frac{a}{b}:=\sqrt[b]{{x}^a}.$ For example $8^{\frac{2}{3}}=\sqrt[3]{{8}^2}=4.$

Number : A number $x$ is a mathematical symbol representing a quantity.

Power : A power is a number of the form $a^b.$ $b$ is called the exponent of the power and $a^b$ is called a power of $a$. For natural numbers $b$ the number $a^b$ is an abbreviation for successively multiplying $a$ by itself $b$ times. For example $2^3=2\cdot 2\cdot 2=8.$ For fractional exponents $b=\frac{p}{q}$ the number $a^{\frac{p}{q}}$ is defined as $\sqrt[q]{a^p}.$ For arbitrary real exponents $b$ the power $a^b$ is defined as the limit of $a^{b_n}$ with rational $b_n$ that converge towards $b.$

Ten thousand : Ten thousand refers to the number $10,000=10^4.$

Thousand : Thousand refers to the number $1,000=10^3.$