By Freddy Van Oystaeyen, Stefaan Caenepeel

According to the court cases of the lately held convention on the loose collage of Brussels, Belgium. presents over 270 references. Softcover.

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**Extra info for Hopf algebras and quantum groups: proceedings of the Brussels conference**

**Example text**

Of course, the situation there was not symmetrical: we could always count steps up but we could not always count steps down. But there would have been no point counting at the same time three steps up and five steps down since steps up would cancel out steps down and this would have just amounted to counting two steps down. EXAMPLE 2. – Actions that a businesswoman may take on a bank account are to deposit three thousand dollars, withdraw two thousand dollars, etc – Actions that a gambler may take are to win fifty-eight dollars, lose sixty-two dollars, etc – Actions that a mark may take on a horizontal line include moving two feet leftward, five feet rightward, etc.

At least in this type of situation. ) EXAMPLE 7. To subtract Jill’s 5 Washingtons from Jack’s 3 Washingtons, that is to identify the specifying-phrase 3 Washingtons − 5 Washingtons But, to identify the specifying-phrase, we would have to start from 3 and count down by a length of 5 but, by the time we got to 0, we would have counted only by a length of 3 and so we cannot complete the count which is as it should be. 4 Subtraction As Correction Subtraction often comes up after we have done a long string of additions and realized that there is an outcast, that is a number-phrase that we shouldn’t have added (for whatever reason), so that, as a consequence, the total is incorrect.

Quite often, though and as we will see in many different situations, the numerator 1 “goes without saying”. EXAMPLE 31. 9. DECIMAL NUMBER-PHRASES 17 DEFAULT RULE # 1. When there is no numerator in front of a denominator and it is otherwise clear that we are dealing with a counting numberphrase, it then goes without saying that the numerator is understood to be 1. NOTE. Unfortunately, this default rule is often abbreviated as “when there is no numerator, the numerator is 1” which is dangerous because when we say that there is no numerator it is tempting to think that the numerator is 0!