The equivalent symbol is used in modular arithmetic to express that two numbers are congruent modulo some number . Typically, the symbol is used in an expression like this:
This expression is used to mean three things:
- evenly divides
- and differ by a multiple of
The equivalent symbol is also used in math to express an identity where the equality is true whichever values are given to the variables occurring within it. For example, the symbol is used in the definition of radians shown below.
This expression means the radian angle is equivalent to any of the values that the arc-length and the radius of the circle take on. For example, if two circles of different radii are used to measure the same angle, the ratio of arc length to radius will be the same.
The equals symbol or equal sign is used in mathematics to assert that two expressions have the same value. It is also used in boolean logic as an operator, evaluating to true or false based on the two input expressions.
The modulus operator returns the remainder of dividing the first expression by the second expression.