View source for zmaumce

==== valsi ====
zmaumce
==== type ====
fu'ivla
==== creator ====
[[personal/krtisfranks|krtisfranks]]
==== time entered ====
Thu Apr  7 01:06:17 2016
 
== English ==
=== Definition #68575 - Preferred ===
 
==== definition ====
x<sub>1</sub> (li) is a bound on set x<sub>2</sub> (set) in direction x<sub>3</sub> (li) in ordered structure x<sub>4</sub>; x<sub>1</sub> bounds x<sub>2</sub> from the x<sub>3</sub> side in x<sub>4</sub>; x<sub>2</sub> is bounded from the x<sub>3</sub> side by x<sub>1</sub>.
==== notes ====
x<sub>2</sub> should be a subset (not necessarily proper) of the set underlying x<sub>4</sub>; it may contain element which are infinite, in general. A bound on a function is really a bound on the image (set; x<sub>2</sub>) of the function's domain set under the operation of the function; otherwise, it is sumti-raising. x<sub>3</sub> accepts either a directional vector (normalized) / a point on the unit circle (in which case the direction from the origin to that point is the direction which is being considered), or exactly one of li [[ma'u|ma'u]] and li [[ni'u|ni'u]]; it is unlikely that any other input would be acceptable.  "[[ma'u|ma'u]]" causes the bound to be an upper bound (a bound on the positive side or the 'right'/'above' when plotted using typical Western European conventions) - it is a number which exceeds/is greater than or equal to every element of x<sub>2</sub> in the set underlying x<sub>4</sub> according to the order endowing x<sub>4</sub>. "[[ni'u|ni'u]]" causes the bound to be an lower bound (a bound on the negative side or the 'left'/'below' when plotted using typical Western European conventions) - it is a number which is less than or equal to every element of x<sub>2</sub> in the set underlying x<sub>4</sub> according to the order endowing x<sub>4</sub>. In order to be well-defined, all elements of x<sub>2</sub> united with the singleton of x<sub>1</sub> must be ordered according to the ordering endowing x<sub>4</sub>; if x<sub>4</sub> lacks a good order, then x<sub>1</sub> is undefined. x<sub>4</sub> must be an ordered structure, not simply a set. Warning: If x<sub>3</sub> is explicitly filled, that is the only direction which is to be assumed.  If it is not explicitly filled, only one (or, arguably, possibly zero) direction(s) is(/are) to be assumed; in this context, it is to be inferred that the set x<sub>2</sub> is (possibly) bounded on at least one side/in at least one direction.  Connecting arguments by 'AND' in x<sub>3</sub> implies that x<sub>2</sub> is the set formed by the singleton of x<sub>3</sub>; it is NOT the equivalent to the English term "bound(ed)" without qualifiers/adjectives (for that meaning, use modulus/absolute value/norm on the input of x<sub>1</sub>). The bound is not strict (proposal: use [[praperi|praperi]] for this sense), but must be true of all elements of x<sub>2</sub> in that direction (x<sub>3</sub>); it is not necessarily the extremal/best finite bound on x<sub>2</sub>. x<sub>1</sub> is typically finite; submitting any infinity for it is arguably bad form but would imply that no element of x<sub>2</sub> is infinite on the side determined by x<sub>3</sub> (where "infinite" has meaning determined also by x<sub>4</sub>; again, for "finite", use modulus/absolute value/norm) - no other information (about its being bounded or unbounded) can be discerned (unless the sumti in x<sub>3</sub> and/or x<sub>4</sub> are incompatible). For explicit statement of unboundedness (in a more general sense, possibly including ill-definition of what "boundedness" even means in this context) in the direction determined by x<sub>3</sub>, use [[zi'au|zi'au]] as the sumti of x<sub>1</sub> (confer earlier note about compatibility of definition and ordering of x<sub>4</sub> with x<sub>2</sub>). x<sub>4</sub> can be more exotic than simply the field of real numbers.
==== gloss words ====

<ul><li>[[natlang/en/bounded set|bounded set ; on a side]]</li><li>[[natlang/en/lower bound|lower bound ; bound below]]</li><li>[[natlang/en/set of only finite elements|set of only finite elements]]</li><li>[[natlang/en/unbounded set|unbounded set]]</li><li>[[natlang/en/upper bound|upper bound ; bound above]]</li></ul>

==== created by ====
[[personal/krtisfranks|krtisfranks]]
==== vote information ====
1
     
==== time ====
Thu Apr  7 01:29:18 2016



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=== Etymology ===