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2. Binary operation - Wikipedia

   en.wikipedia.org/wiki/Binary_operation

   Typical examples of binary operations are the addition (+) and multiplication of numbers and matrices as well as composition of functions on a single set. For instance, For instance, On the set of real numbers R {\displaystyle \mathbb {R} } , f ( a , b ) = a + b {\displaystyle f(a,b)=a+b} is a binary operation since the sum of two real numbers ...

3. Commutative property - Wikipedia

   en.wikipedia.org/wiki/Commutative_property

   Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction , that do not have it (for example, "3 − 5 ≠ 5 − 3" ); such operations are not commutative, and so are ...

4. Addition - Wikipedia

   en.wikipedia.org/wiki/Addition

   A number-line visualization of the algebraic addition 2 + 4 = 6. A "jump" that has a distance of 2 followed by another that is long as 4, is the same as a translation by 6. A number-line visualization of the unary addition 2 + 4 = 6. A translation by 4 is equivalent to four translations by 1.

5. Arithmetic - Wikipedia

   en.wikipedia.org/wiki/Arithmetic

   Example of modular arithmetic using a clock: after adding 4 hours to 9 o'clock, the hand starts at the beginning again and points at 1 o'clock. 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 ...

6. Elementary arithmetic - Wikipedia

   en.wikipedia.org/wiki/Elementary_arithmetic

   Example of addition with carry. The black numbers are the addends, the green number is the carry, and the blue number is the sum. In the rightmost digit, the addition of 9 and 7 is 16, carrying 1 into the next pair of the digit to the left, making its addition 1 + 5 + 2 = 8. Therefore, 59 + 27 = 86.

7. Identity element - Wikipedia

   en.wikipedia.org/wiki/Identity_element

   In mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. [1] [2] For example, 0 is an identity element of the addition of real numbers. This concept is used in algebraic structures such as groups and rings.