From: "Apache" <apache@digitalkingdom.org>
To: curtis289@att.net
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Subject: [jvsw] Definition Added At Word zmaumce -- By krtisfranks
Date: Wed, 6 Apr 2016 18:06:17 -0700
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 Content preview:  In jbovlaste, the user krtisfranks has added a definition
   of "zmaumce" in the language "English". New Data: Definition: $x_1$ (li) is
    a bound on set $x_2$ (set) in direction $x_3$ (li) in ordered structure $x_4$;
    $x_1$ bounds $x_2$ from the $x_3$ side in $x_4$; $x_2$ is bounded from the
    $x_3$ side by $x_1$. [...] 
 
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In jbovlaste, the user krtisfranks has added a
definition of "zmaumce" in the language "English".

New Data:

	Definition:
		$x_1$ (li) is a bound on set $x_2$ (set) in direction $x_3$ (li) in ordered structure $x_4$; $x_1$ bounds $x_2$ from the $x_3$ side in $x_4$; $x_2$ is bounded from the $x_3$ side by $x_1$.

	Notes:
		A bound on a function is really a bound on the image (set; $x_2$) of the function's domain set under the operation of the function; otherwise, it is sumti-raising. $x_3$ 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 $x_2$ in the set underlying $x_4$ according to the order endowing $x_4$. "{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 $x_2$ in the set underlying $x_4$ according to the order endowing $x_4$.  Warning: If $x_3$ 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 $x_2$ is (possibly) bounded on at least one side/in at least one direction.  Connecting arguments by 'AND' in $x_3$ implies that $x_2$ is the set formed by the singleton of $x_3$; 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 $x_1$). The bound is not strict (proposal: use {praperi} for this sense), but must be true of all elements of $x_2$ in that direction ($x_3$); it is not necessarily the extremal/best finite bound on $x_2$. $x_1$ is typically finite; submitting any infinity for it is arguably bad form but would imply that no element of $x_2$ is infinite on the side determined by $x_3$ (where "infinite" has meaning determined also by $x_4$; again, for "finite", use modulus/absolute value/norm) - no other information (about its being bounded or unbounded) can be discerned (unless the sumti in $x_3$ and/or $x_4$ are incompatible). For explicit statement of unboundedness, use {zi'au} as the sumti of $x_1$. $x_4$ can be more exotic than simply the field of real numbers.

	Jargon:
		

	Gloss Keywords:
		Word: upper bound, In Sense: bound above
		Word: lower bound, In Sense: bound below
		Word: bounded set, In Sense: on a side
		Word: set of only finite elements, In Sense: 
		Word: unbounded set, In Sense: 

	Place Keywords:


You can go to <http://jbovlaste.lojban.org/dict/zmaumce> to see it.