Identity and conditional equations are ways in which numbers associate with each other. When an equation is true for every value of the variable, then the equation is called an identity equation. It is often denoted as I or E (the E is from the German Einheit, or “unity”). For example, 3x = 3x is an identity equation, because x will always be the same number. Zero is the identity element for addition, because any number added to 0 does not change the value of any of the other numbers in the operation (or x + 0 = x). The number 1 is the identity element of multiplication, as any number in an operation multiplied by 1 does not change the value of that number. Multiple identity is often written as x × 1 = x.

When an equation is false for at least one value, it is called a conditional equation. For example, 6x = 12 is conditional because it is false when x = 3 (and any number other than 2). In other words, if at least one value can be found in which the equation is false (or the right side is not equal to the left side) then the equation is called a conditional equation.