By Avramov L.L. (ed.), Tchakerian K.B. (ed.)
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This booklet takes a distinct method of details retrieval by way of laying down the rules for a contemporary algebra of data retrieval in response to lattice concept. All significant retrieval equipment constructed thus far are defined intimately – Boolean, Vector house and probabilistic equipment, but additionally net retrieval algorithms like PageRank, HITS, and SALSA – and the writer exhibits that all of them should be handled elegantly in a unified formal means, utilizing lattice concept because the one simple thought.
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Extra resources for Algebra Some Current Trends
Can the set N represent any number at all? We can never finish writing the list of its elements. But the mere fact that we can’t write the whole list doesn’t mean that the set itself does not exist. We can imagine it, so in the mathematical world, it exists! Mathematicians define the number represented by the entire set N as a form of “infinity” and denote it using the last letter in the Greek alphabet, omega, in lowercase (ω). ” In formal terms, ω is called an infinite ordinal or transfinite ordinal, and it has some strange properties.
In theory, those elements could be anything, such as apples, stars, atoms, or people. But it’s convenient to use all the natural numbers less than p as those elements. That allows us to build the set of natural numbers, one on top of the other, like stacking coins. Just as each coin in the stack rests on all the coins below itself, every element p in the set of natural numbers “rests on” all the natural numbers “below” itself. Once this process is defined, it sets in motion a mathematical “chain reaction” that never ends.
Algebra Some Current Trends by Avramov L.L. (ed.), Tchakerian K.B. (ed.)