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  2. 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.

  3. Proofs involving the addition of natural numbers - Wikipedia

    en.wikipedia.org/wiki/Proofs_involving_the...

    We prove associativity by first fixing natural numbers a and b and applying induction on the natural number c.. For the base case c = 0, (a + b) + 0 = a + b = a + (b + 0)Each equation follows by definition [A1]; the first with a + b, the second with b.

  4. Group (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Group_(mathematics)

    For example, the integers with the addition operation form an infinite group, which is generated by a single element called ⁠ ⁠ (these properties characterize the integers in a unique way). The concept of a group was elaborated for handling, in a unified way, many mathematical structures such as numbers, geometric shapes and polynomial roots .

  5. Addition - Wikipedia

    en.wikipedia.org/wiki/Addition

    For example, the set of integers modulo 12 has twelve elements; it inherits an addition operation from the integers that is central to musical set theory. The set of integers modulo 2 has just two elements; the addition operation it inherits is known in Boolean logic as the " exclusive or " function.

  6. Carry (arithmetic) - Wikipedia

    en.wikipedia.org/wiki/Carry_(arithmetic)

    A typical example of carry is in the following pencil-and-paper addition: 1 27 + 59 ---- 86 7 + 9 = 16, and the digit 1 is the carry. The opposite is a borrow, as in −1 47 − 19 ---- 28 Here, 7 − 9 = −2, so try (10 − 9) + 7 = 8, and the 10 is got by taking ("borrowing") 1 from the next digit to the left. There are two ways in which ...

  7. Integer - Wikipedia

    en.wikipedia.org/wiki/Integer

    For example, 21, 4, 0, and −2048 are integers, while 9.75, ⁠5 + 1 / 2 ⁠, 5/4, and √ 2 are not. [8] The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers.

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