Term for this concept

For the discussion of math. Duh.

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Quizatzhaderac
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Term for this concept

Postby Quizatzhaderac » Tue Apr 28, 2015 2:55 pm UTC

A is the powerset of B.
That makes B a <?> set of A.

For example a byte can represent [0,255] and it's set of on bits could be represented as members of the universe {a,b,c,d,e,f,g,h}. So {a,c,g} -> 162, just as anything in [0,255] can be mapped to an element of the powerset of [a,g]
The thing about recursion problems is that they tend to contain other recursion problems.

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Qaanol
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Re: Term for this concept

Postby Qaanol » Tue Apr 28, 2015 5:57 pm UTC

I don’t know if there’s an official term for it, but “Generating set” seems to capture the idea, as in B generates A (under the “Union” operation on its members-treated-as-singletons).
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Tirian
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Re: Term for this concept

Postby Tirian » Tue Apr 28, 2015 8:16 pm UTC

Quizatzhaderac wrote:For example a byte can represent [0,255] and it's set of on bits could be represented as members of the universe {a,b,c,d,e,f,g,h}. So {a,c,g} -> 162, just as anything in [0,255] can be mapped to an element of the powerset of [a,g]


That paragraph is reasonably clear. If you added a sentence with <?> because you don't know which word to use in its place, we might be able to give more specific help.

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Quizatzhaderac
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Re: Term for this concept

Postby Quizatzhaderac » Tue Apr 28, 2015 9:37 pm UTC

Example for Tirian:

The integers in [0,255] map to the powerset of [a,g].
[a,g] maps to the <?> set of [0,255]

Qaanol is right in that this is a specific case of a generating set.
The thing about recursion problems is that they tend to contain other recursion problems.

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notzeb
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Re: Term for this concept

Postby notzeb » Tue Apr 28, 2015 10:50 pm UTC

"Maximal element (under containment)" works, if you throw out the word "set" after it. "Union" works, if you interpret union as in the axiom of union. "Base 2 logarithm" seems to be what you really want, but I don't think anyone calls it that.
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Quizatzhaderac
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Re: Term for this concept

Postby Quizatzhaderac » Wed Apr 29, 2015 7:10 pm UTC

I know I used numbers and letters in my examples, but I didn't intent to imply the elements needed to be order-able. An example with elements that aren't order-able.
Let A be the set of perceived colors {black,red,green,blue,yellow,purple, turquoise, white}
Let B be be the set of sensed colors {red,green, blue}

Each of the perceived colors corresponds to a set of sensed colors
{{null},{red},{green},{blue},{red,green},{red,blue},{green, blue},{red,green,blue}}
Last edited by Quizatzhaderac on Fri Jul 01, 2016 3:22 pm UTC, edited 1 time in total.
The thing about recursion problems is that they tend to contain other recursion problems.

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Cleverbeans
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Re: Term for this concept

Postby Cleverbeans » Wed Apr 29, 2015 7:14 pm UTC

I think we should call it the logset.
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Tirian
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Re: Term for this concept

Postby Tirian » Wed Apr 29, 2015 8:33 pm UTC

If I were writing these concepts, I would describe the primary colors as factors in the spectrum of visual light, or the eight bits as all the factors in the value of a byte. It isn't so nonstandard a use if you consider that the evaluation function is an isomorphism between the powerset of S and 2S (which is, in fact, the old-school notation for the powerset).

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z4lis
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Re: Term for this concept

Postby z4lis » Wed Apr 29, 2015 10:02 pm UTC

There's a unary union operator in set theory defined by UX = {elements of elements of X} which satisfies UPX = X, and so gives a left inverse of the powerset. So A = PB implies UA = B. However, it doesn't go the other way.
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