Without loss of general information
Without loss of general information (or also: without restricting the general information ) is an expression frequently used in the Démonstration S in Mathématiques. This expression, generally followed by a restrictive assumption, indicates that the demonstration is limited to a particular case, but that the other cases can be establish by a demonstration similar to that of the case considered, or to even bring back itself to this case.
Other expressions like “without harming the general information”, have the same significance.
Example
Proposal:
A definite function F and continues on the interval, such as F ( has )· F ( B ) < 0, is cancelled at least once in '' B.
Demonstration:
Assumption F ( has )· F ( B ) < 0, it follows that F ( has ) and F ( B ) is signs opposés.
Without loss of general information , we consider only the case where F ( has ) < 0 and F ( B ) > 0.
Comes then the demonstration from this particular case.
The other case is reduced to the precedent: it is enough to consider the opposite function - F .
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