section_path: Types/Others
section_name: Others
paragraph_text: Others
  
  There are many other types of arithmetic. Modular arithmetic operates on a finite set of numbers. If an operation would result in a number outside this finite set then the number is adjusted back into the set, similar to how the hands of clocks start at the beginning again after having completed one cycle. The number at which this adjustment happens is called the modulus. For example, a regular clock has a modulus of 12. In the case of adding 4 to 9, this means that the result is not 13 but 1. The same principle applies also to other operations, such as subtraction, multiplication, and division.
  
  Some forms of arithmetic deal with operations performed on mathematical objects other than numbers. Interval arithmetic describes operations on intervals. Vector arithmetic and matrix arithmetic describe arithmetic operations on vectors and matrices, like vector addition and matrix multiplication.
  
  Arithmetic systems can be classified based on the numeral system they rely on. For instance, decimal arithmetic describes arithmetic operations in the decimal system. Other examples are binary arithmetic, octal arithmetic, and hexadecimal arithmetic.
  
  Compound unit arithmetic describes arithmetic operations performed on magnitudes with compound units. It involves additional operations to govern the transformation between single unit and compound unit quantities. For example, the operation of reduction is used to transform the compound quantity 1 h 90 min into the single unit quantity 150 min.
  
  Non-Diophantine arithmetics are arithmetic systems that violate traditional arithmetic intuitions and include equations like 1 + 1 = 1 {\displaystyle 1+1=1} and 2 + 2 = 5 {\displaystyle 2+2=5}. They can be employed to represent some real-world situations in modern physics and everyday life. For instance, the equation 1 + 1 = 1 {\displaystyle 1+1=1} can be used to describe the observation that if one raindrop is added to another raindrop then they do not remain two separate entities but become one.