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]

## Term for this concept

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- Quizatzhaderac
**Posts:**1821**Joined:**Sun Oct 19, 2008 5:28 pm UTC**Location:**Space Florida

### Term for this concept

The thing about recursion problems is that they tend to contain other recursion problems.

### Re: Term for this concept

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).

wee free kings

### Re: Term for this concept

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.

- Quizatzhaderac
**Posts:**1821**Joined:**Sun Oct 19, 2008 5:28 pm UTC**Location:**Space Florida

### Re: Term for this concept

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 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.

### Re: Term for this concept

"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
**Posts:**1821**Joined:**Sun Oct 19, 2008 5:28 pm UTC**Location:**Space Florida

### Re: Term for this concept

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}}

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.

- Cleverbeans
**Posts:**1378**Joined:**Wed Mar 26, 2008 1:16 pm UTC

### Re: Term for this concept

I think we should call it the logset.

"Labor is prior to, and independent of, capital. Capital is only the fruit of labor, and could never have existed if labor had not first existed. Labor is the superior of capital, and deserves much the higher consideration." - Abraham Lincoln

### Re: Term for this concept

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 2

^{S}(which is, in fact, the old-school notation for the powerset).### Re: Term for this concept

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.

What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.

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