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valsi zmaumce
type fu'ivla
creator krtisfranks
time entered Thu Apr 7 01:06:17 2016

Definition #68575 - Preferred [edit]
definition x1 (li) is a bound on set x2 (set) in direction x3 (li) in ordered structure x4; x1 bounds x2 from the x3 side in x4; x2 is bounded from the x3 side by x1.
notes x2 should be a subset (not necessarily proper) of the set underlying x4; it may contain element which are infinite, in general. A bound on a function is really a bound on the image (set; x2) of the function's domain set under the operation of the function; otherwise, it is sumti-raising. x3 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 and li ni'u; it is unlikely that any other input would be acceptable. "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 x2 in the set underlying x4 according to the order endowing x4. "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 x2 in the set underlying x4 according to the order endowing x4. In order to be well-defined, all elements of x2 united with the singleton of x1 must be ordered according to the ordering endowing x4; if x4 lacks a good order, then x1 is undefined. x4 must be an ordered structure, not simply a set. Warning: If x3 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 x2 is (possibly) bounded on at least one side/in at least one direction. Connecting arguments by 'AND' in x3 implies that x2 is the set formed by the singleton of x3; 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 x1). The bound is not strict (proposal: use praperi for this sense), but must be true of all elements of x2 in that direction (x3); it is not necessarily the extremal/best finite bound on x2. x1 is typically finite; submitting any infinity for it is arguably bad form but would imply that no element of x2 is infinite on the side determined by x3 (where "infinite" has meaning determined also by x4; again, for "finite", use modulus/absolute value/norm) - no other information (about its being bounded or unbounded) can be discerned (unless the sumti in x3 and/or x4 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 x3, use zi'au as the sumti of x1 (confer earlier note about compatibility of definition and ordering of x4 with x2). x4 can be more exotic than simply the field of real numbers.
gloss words
created by krtisfranks
vote information 1
time Thu Apr 7 01:29:18 2016


krtisfranks{zmadu} + {mleca}[edit]
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