Subtraction
The subtraction is one of the basic operations of the Arithmétique. The subtraction combines two or several sizes of the same type, called operands , to give only one number, called the difference .
- Soustraire means to decrease while counting.
- Soustraire B of has (to calculate has − b) is to find the number which would supplement B to give has, i.e. the number D such as B + D = has
General standard
That is to say ( G , +) a additive group. One defines a news Law of composition interns in G , called “subtraction” and noted “ − ” by :
- X − there = X + (- there )
Particular case of the numbers
Here we work in (, +), the additive group of the relative integers .Formally, the subtraction is a law of composition interns on a unit, noted - in condition however that the subtraction is always defined (what is not, for example, the case in the whole of the natural entireties ). This internal law of composition (when it exists) is however not very interesting because
- it is not commutative. Indeed has − B and B − has are in general different
- it is not associative. Indeed (− b) − C has and has − (B − c) are in general different
- it does not have a neutral element. Indeed, the only possible neutral element would be 0 and one has well
This is why one prefers to consider a subtraction as the addition (nap) of opposed to condition obviously that this opposite exists (it is not always the case in ).
- the opposite of has is the number noted (−a) which, added to has, gives 0: + (−a) has = 0
- has − B can then be written has + (−b)
When it is applied to a series as in Algorithmique it is a decrement .
See also: tax Subtraction
Simple: Subtraction
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