Second, if we have to say a rough and simple method, it is: "total * * *, one * * *" and other topics, using addition, "the rest, the rest, and" using subtraction.
Addition has several important properties. It is interchangeable, which means that the order is not important, it is interrelated, which means that when more than two numbers are added, the order in which the addition is performed is not important. Repeatedly adding 1 is the same as counting; Adding 0 will not change the result. Addition also follows related operations such as subtraction and multiplication.
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Subtraction follows several important patterns. It is anti-commutative, which means that changing the order will change the sign of the answer. It is not associative law, that is, when a subtraction exceeds two numbers, the order of subtraction is very important. Subtracting 0 does not change a number. Subtraction also follows predictable rules related to addition and multiplication.
These laws can be proved, starting with the subtraction of integers and summarizing them with real numbers and other things. Continue the general binary operation of these patterns and learn in abstract algebra.
The way to increase natural numbers is to add ordinal numbers and cardinality to set theory. These give two different generalizations, namely, natural numbers. Unlike most addition operations, ordinal addition is not interchangeable. However, increasing cardinality is an exchange operation closely related to disjoint union operation.
In category theory, disjoint addition is considered as a special case, which may generally be the most abstract of all addition generalizations. For example, direct sum and wedge sum are called adding links.
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