It takes the average reader 3 hours and 29 minutes to read Cardinalities of Fuzzy Sets by Maciej Wygralak
Assuming a reading speed of 250 words per minute. Learn more
Counting is one of the basic elementary mathematical activities. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over. For finite sets of objects these two aspects are realized by the same type of num bers: the natural numbers. That these complementary aspects of the counting pro cess may need different kinds of numbers becomes apparent if one extends the process of counting to infinite sets. As general tools to determine numbers of elements the cardinals have been created in set theory, and set theorists have in parallel created the ordinals to count over any set of objects. For both types of numbers it is not only counting they are used for, it is also the strongly related process of calculation - especially addition and, derived from it, multiplication and even exponentiation - which is based upon these numbers. For fuzzy sets the idea of counting, in both aspects, looses its naive foundation: because it is to a large extent founded upon of the idea that there is a clear distinc tion between those objects which have to be counted - and those ones which have to be neglected for the particular counting process.
Cardinalities of Fuzzy Sets by Maciej Wygralak is 205 pages long, and a total of 52,275 words.
This makes it 69% the length of the average book. It also has 64% more words than the average book.
The average oral reading speed is 183 words per minute. This means it takes 4 hours and 45 minutes to read Cardinalities of Fuzzy Sets aloud.
Cardinalities of Fuzzy Sets is suitable for students ages 12 and up.
Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.
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