# zi'au KOhA experimental cmavo

nonexistent/undefining it; the selbri is not applicable when the other terbri are filled in the manner in which they are in this utterance/bridi.

In words for math which have a terbri for the result of an operation, filling that terbri with this word indicates not that the operation evaluates but rather that the operation cannot be applied to the given inputs at all; the operation on those inputs is undefined or has no existing well-defined solution(s). Given the other sumti in the predicate (filling the corresponding terbri), the underlying relation (selbri) is claimed to be invalid in this circumstance. Examples: "non-integrable", "non-measurable" (confer: ".umre"), "non-summable" (say, of strings), "the limit does not exist". This avoids the necessity of creating a pair of words for every such mathematical concept (one for when the operation may be applied to the inputs so as to yield a well-defined value which may be specified and one for when such is not the case). Other uses may develop or be found. This word does not 'delete' the terbri (unlike "zi'o"); it simply says that the selbri is not really applicable. Whether or not the meaning of this word is within the generic semantic range of "zo'e" is debatable and not yet well-established. The conventions employed matter. The case of the product of zero and infinity usually must be handled by a separate definition (especially when dealing only with strictly real numbers); it is quite common to explicitly handle this case by defining the product as zero, but prior to such definition, "lo pilji be li no bei li ci'i" is meaningless and undefined (the symbols can be written but do not actually mean anything) - so, pilji1 should be filled with this word in such a circumstance. As another example, unless the difference of infinity with infinity is defined (and following the convention that unconnected points have a graph distance of positive countable infinity), which is unnatural, the relationship represented by "tseingu" is undefined in its fourth terbri (so, it can be filled with this word) when its first and second sumti belong to mutually different trees (leaving their most recent mutually common ancestor undefined). Notice that the other terbri are well-defined in this circumstance - in particular, tseingu3 is positive countable infinity; also notice that this word has a slightly less mathematical flavor (especially insofar as the first terbri is not result of applying a mathematical operation to the following terbri) than many other ready examples. Yet another example: In a zero-dimensional universe, klama4 and possibly klama5, as well as even more arguably klama2, are undefined (and can be filled with this word), leaving the notion of 'going' empty and meaningless. In a (-1)-dimensional universe (an empty set), every terbri of "klama" (and probably every other word) is undefined and can be filled with this terbri.

## In notes:

tseingu
x1 (node in a tree graph) and x2 (node in the same tree graph) have an essentially unique most recent (graph-nearest) common ancestor node A such that x3 [nonnegative integer; li] is the minimum element of the set consisting only of d(A, x1) and of d(A, x2), and such that x4 [integer; li] is d(A, x1) - d(A, x2), where d is the graph geodesic distance (defined to be infinite if nodes are not connected in the correct direction).
zmaumce
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.