x_{1} [quantifier/expression] is a mathematical expression interpreted under rules/convention x_{2}.

See also cmaci, dilcu, fancu, frinu, jalge, namcu, parbi, pilji.

- tu'o
- null operand (used in unary mekso operations).
- su'ifa'uvu'u
- mekso operator: plus or minus with order important, (((a±b)±c)±...±z)
- su'ijavu'u
- mekso operator: plus or minus, (((a±b)±c)±...±z)
- bai'i
- mekso string operator (ternary): find-and-replace; in string/text/word/sequence X1 formally replace X2 (ordered tuple of terms to be replaced) with X3 (ordered tuple of terms to be respectively substituted)
- bai'i'i
- mekso operator: in ordered tuple/list/vector/sequence X
_{1}, replace the X_{2}th entry with term X_{3}of appropriate type, and leave all other entries untouched (optional: where the index for the very first/leading/header entry is X_{4}). - be'ei'oi
- ternary mekso operator: x
_{1}th Bergelson multiplicative interval with exponents bounded from above by function x_{2}and with sequence of shifts x_{3}, where exponents belong to set x_{4} - bei'u'i
- unary mekso operator: nth Bernoulli number B
_{n}of the second kind (B_{1 }= +1/2 = >0). - boi'ai
- unary mekso operator: immediately convert number into a single digit.
- boi'e'u
- mekso operator/function terminator (in Polish notation): inserts exactly enough "{boi}"'s consecutively so as to terminate the most recently uttered operator/function in a mekso expression
- boi'oi
- preserve formal interpretation of mekso subexpression with no substitutions made
- ca'ei'a
- Unary mekso operator: unit vector/normalization of the argument (vector) X.
- ca'o'e
- mekso 4-nary operator: spherical harmonics on colatitudinal/polar angle a and azimuthal/longitudinal angle b of unassociated order c and associated order d.
- ci'ai'u
- Mekso unary or binary operator: n-set or integer interval; in unary form, it maps a nonnegative integer X
_{1 }= n to the set \1, \dots , n\ (fully, officially, and precisely: the intersection of (a) the set of exactly all positive integers with (b) the closed ordered interval [1, n] such that n \geq 1; see notes for other n); in binary form, it maps ordered inputs (X_{1, X}= (m, n) to the intersection of (a) the set of exactly all integers with (b) the closed ordered interval [m, n]. - ci'au'i
- mekso at-most-4-ary operator: integer lattice ball; the set of all points belonging to the intersection of Z
^{n}with the closure of the ball that is centered on X_{1}and has radius X_{2}in metric X_{3}, where Z is the set of all integers and where, for any set A and non-negative integer n, A^{n}is the set of all n-tuples such that each coordinate/entry/term belongs to A, and where the dimensionality n = X_{4}.. - ci'o'au
- mekso operator (binary): projection function; the Bth term/entry ("element") of tuple A
- cu'au'ei
- mekso binary/unary operator: multinomial coefficient/binomial coefficient/choose
- da'a'au
- mekso operatory: prime mark append
- de'au'u
*(exp!)* - mekso ternary operator: positive super-logarithm; the super-logarithm (inverse operator of hyper-operator with respect to "height" of power tower) of a with base b and of order c-2.
- dei'au'o
- mekso binary operator: Lambert product-log W function; W(a, b)
- du'a'e
- mekso n-ary ordered operator: structure creator/ordered tuple, 'endow'; the structure formed by underlying set X
_{1}(as) endowed with element, order, quoted operator, etc. X_{2}, X_{3}, ... - du'a'o
- mekso binary operator: extract substructure/underlying set/endowing operator; the substructure (general sense; includes just operator, order, set, etc.) of X
_{1}(structure; explicitly given by {du'a'e}) which is formed by collecting the ith entries of that {du'a'e}-tuple in order together into their own {du'a'e}-tuple (or by extracting them naked into the ambient environment if X_{2}is a singleton) for all i in set X_{2} - du'ei
- mekso binary operator: left-handed vectorial cross product (ordered input), -a \times b = b \times a (if using right-hand convention - notice the negative sign/operator or order).
- fa'ai'ai
- mekso k-ary operator, for natural k and 1 < k < 5: ordered input (f, g, S, m) where f and g are functions, S is a set of positive integers or "ro" (="all"), and m is 0 or 1 (as a toggle); output is a function equivalent to the function f as applied to an input ordered tuple with g applied to the entries/terms with indices in S (or to all entries/terms if S="ro") if m=0, or g left-composed with the same if m=1.
- fa'ei
- Unary mekso operator: reverse finite ordered sequence, tuple, list, string, etc.
- fau'i
- mekso ternary operator: inverse function of input function X
_{1}with respect to its input X_{2}, taken on branch or restricted domain X_{3}("domain" being of X_{1}). - fe'au'u
*(exp!)* - mekso ternary operator: positive super-root; the bth super-root (inverse operator of hyper-operator with respect to base) of a of order c-2.
- fe'ei
- binary mekso operator: divided by (fraction): a/(b...)
- fei'i
*(exp!)* - mekso variable-arity (at most ternary) operator: number of prime divisors of number X
_{1}, counting with or without multiplicity according to the value X_{2}(1 xor 0 respectively; see note for equality to -1 and for default value), in structure X_{3}. - fi'au
- mekso operator: continued fraction, Kettenbruch notation; for ordered input (X
_{1, X}, where: X_{1}is an ordered pair of functions and X_{2}is a free or dummy variable/input/index which ranges through set X_{3}in order(ing) X_{4}, the result is K_{(X}for Kettenbruch notation K. - ga'ai
- unary mekso operator: Lorentz-Einstein gamma factor +1/((1-(|X|
^{2))}for input X. - gau'a
- mekso (no-more-than-4-ary) operator: Gaussian function f(x, a, b, c) = c e
^{-((x-a)}. - ga'u'au
- mekso n-ary operator: append contravariant (upper) indices to tensor
- gei'au
*(exp!)* - mekso 7-ary operator: for input (X
_{1 }= z, X_{2 }= (a_{i)}= (b_{j)}= p, X_{5 }= q, X_{6 }= h_{1, X}= h_{2)}, this word/function outputs/yields \sum_{n}=0^\infty (((\prod_{i }= 1^{p (}ne'o'o(a_{i,n,1,h}= 1^{q (}ne'o'o(b_{j,n,1,h}; by default, X_{6 }= 1 = X_{7}unless explicitly specified otherwise. - gei'i'e
- mekso unary operator: converts a string of digits which includes {pi} to the same string of digits without {pi}; if {pi} is not present in the original/input string, the output is identical
- gu'au'i
- mekso operator, variable arity - algebraic structure order of X1; OR: order of/(size of) period of element X1 in algebraic structure X2 under operator/of type X3
- je'e'e
- mekso operator: associated Legendre polynomial in a with unassociated order b and associated order c
- ji'e'ai
- mekso unary operator: determinant, det(A)
- ji'i'u
- mekso, at-most-5-ary operator: a rounding function; ordered input list is (x,n,t,m,b) and the output is sgn(x) b
^{t}round_{n}(b^{(-t)}abs(x)), with rounding preference n and where the fractional part of b^{(-t)}abs(x) being equal to 1/2 causes the round_{n (}) function to map b^{(-t)}abs(x) to the nearest integer of form 2Z+m, for base b (determined by context if not explicitly input) and some integer Z (determined by context). - ji'i'u'u
- mekso, at-most-5-ary; rounding function. (See notes).
- jo'ei'i
*(exp!)* - nonlogical connective (and mekso operator) - symmetric difference of sets
- joi'i
- mekso string operator (n-ary): formal right-concatenation; X
_{1 + X}, where X_{i}is a string/word/text/character/letteral/lerfu/quoted utterance (quote appropriately iff necessary; preserve and be careful about the use-vs.-mention distinction) for all i. - ka'au
*(exp!)* - mekso unary operator: cardinality (#, | |)
- kei'ai
- mekso style converter: elementwise application of operator
- kei'au
- mekso operator: finite result set derived from/on set A with/due to operator/function B under ordering of application C
- kei'i
- non-logical connective/mekso operator - of arity only 1 xor 2: set (absolute) complement, or set exclusion (relative complement). Unary: X
_{2 ^C}; binary: X_{1\setminusX}. - ku'au'a
- mekso (n+1)-ary operator: q-analog converter - the ath analog of b (quoted operator) applied to operands c, d, ...
- ku'oi'u
- closing bracket/terminator for mekso expression interpretation modifiers
- lau'au
- mekso unary operator: for input X, this outputs X/(1+X).
- li'ei'au
- ternary mekso operator: retrieves/gets/outputs the X
_{2}th entry/term from ordered list X_{1}under indexing rules X_{3}. - ma'au
- Binary mekso operator: uniform probability A(X
_{2)u(X}for input (X_{1,X}where X_{1}is a number and X_{2}is a set or space. (See notes for details). - mai'u
- unary mekso operator: signum function
- mau'au
- mekso: conversion of operator/function to operand
- me'ei'o
- mekso n-ary operator: interleave sequences
- mu'ai'au
- mathematical/logical/mekso ternary operator: μ (mu) operator: outputs the most extreme extended-natural number that satisfies relationship/predicate A, where extremeness is bounded by B and of a version determined by C; error output is -1
- mu'au
- unary mekso operator: measure of the complement; 1 - x
_{1}. - na'au
*(exp!)* - converts an unevaluated mekso expression into a sumti referencing its evaluated result (if sensible/defined)
- nei'au
- unary mekso operator: (-1)
^{x} - ne'o'a
*(exp!)* - mekso ternary operator: the generalized incomplete (factorial-extending) Pi function; for input (X
_{1, X}this word outputs the definite integral of t^X_{1 e^-t}with respect to t from X_{2}to X_{3}(see notes for default values). - ne'o'au
*(exp!)* - mekso quaternary operator: polygamma function; for input X
_{1, X}, outputs the (-X_{2)}th derivative of Log(ne'o'a(X_{1, X})) with respect to X_{1}. - ne'o'o
*(exp!)* - mekso quaternary operator – Pochhammer symbol: with/for input (X
_{1, X}, this word/function outputs \prod_{k }= 0^X_{2 - 1 (X}; by default, X_{4 }= 1 unless explicitly defined otherwise. - ni'a'au
- mekso n-ary operator: append covariant (lower) indices to tensor
- no'au'au
- mathematical/mekso binary operator: the zero/identity-element/(primitive (-))constant operator; outputs the identity-element of structure A (contextless default: the additive group of integers) regardless of the input value of B (except blank or ill-defined values)
- pau'a'u
- mekso operator: part of number/projection (one sense); the X2 part of X1
- pau'au
*(exp!)* - ternary mekso operator: p-adic valuation; outputs (positive) infinity if x
_{1 }= 0 and, else, outputs sup(Set(k: k is a nonnegative integer, and ((1 - x_{3)x}divides x_{1))}, where p_{n}is the nth prime (such that p_{1 }= 2). - pau'ei
- mekso operator: power set - produces the set of all subsets of set X
_{1}that are of (any) size (that is) X_{2}[a nonnegative integer or transfinite/infinite number; default: su'o no]. - pei'e'a
- at-most-3-ary mekso operator: "integer exponent" for X
_{1}divided by X_{2}in algebraic structure X_{3} - pi'au'e
- mekso ternary operator: extract digit from number; X
_{2}nd macrodigit/term of number/tuple X_{1}when X_{1}is expressed in base/basis X_{3}. - pi'ei
- mathematical/mekso binary operator: vector or function inner product over a field; the inner product of A and B over field C
- pi'u'e
- mekso n-ary operator: generate ordered tuple/list from inputs; pi'u'e(x
_{1, x}= (x_{1, x}, pi'u'e(x_{1, x}= (x_{1, x}, etc. - po'i'ei
*(exp!)* - n-ary mekso operator: for an input of ordered list of ordered pairs ((X
_{1, Y}, it outputs formal generalized rational function (x - X_{1)^Y}in the adjoined indeterminate (here: x). - po'i'oi
- mekso at-most-3-ary operator: convert to polynomial; X
_{1}(ordered list of algebraic structure (probably field) elements) forms the (ordered list of) coefficients of a polynomial/Laurent-like series with respect to indeterminate X_{2}under ordering rule X_{3}(default for finite list: the first entry is the coefficient of the highest-degree term and each subsequent entry is the next lesser-degree coefficient via counting by ones and wherein the last entry is the constant term) - pu'e'ei
*(exp!)* - mekso binary operator: generate span; outputs span(X
_{1, X}= span_{X}; set of all (finite) sums of terms of form c v, where v is an element of algebraic structure X_{1}(wherein scalar multiplication and summation is defined), and c is a scalar belonging to ring X_{2}. - ra'i'e
- ternary mekso/mathematical operator: radical; for input (x,y,z), it outputs the largest y-th-power-free product of prime divisors of x in structure (ring) z.
- rai'i
- mekso (2 or 3)-ary operator: maximum/minimum/extreme element; ordered list of extreme elements of the set underlying ordered set/structure X
_{1}in direction X_{2}of list length X_{3}(default: 1) - sai'ei
*(exp!)* - turns PA into CAI; intensity attitude modifier expressed by a mekso.
- sau'au
*(exp!)* - mekso binary operator: del, nabla, quabla, partial-derivative vector/tensor operator; outputs the functional-valued formal-covector (or analog thereof) of partial derivatives with respect to X
_{1}(tensor in the same format and order), each degree X_{2}(default: 1). - sau'i
- mekso n-ary operator: reciprocal of the sum of the reciprocal of each of X
_{1}, X_{2}, ..., X_{n}(for any natural number n); 1/((1/X_{1) + (1/X}. - si'oi'e
- n-ary mekso operator: Logistical growth/cumulative function, sigmoid function; (X
_{3 / (1 + e^(-X}. - su'i'e
- mekso unary operator: digital addition.
- su'i'o
- mekso unary or binary operator: ordered inputs (n, b) where n and b are nonnegative integers and b > 1; output is the ultimate digital root of n in base-b.
- tai'e'i
- mekso unary operator: basic Schlafli symbol composer (defined only on ordered lists)
- tai'i'au
*(exp!)* - 8-ary mekso operator: the X
_{1}th nonnegative sum of X_{2}mutually-distinct perfect X_{3}th-powers (i.e.: of integers) in X_{4}mutually truly-distinct ways, requiring exactly X_{5}terms to be negative in each sum (counting with(out^X_{6}) multiplicity), requiring exactly X_{7}terms to be repeated between sums (counting with(out^X_{8}) multiplicity), according to the usual ordering of the integers. - tai'i'e
- mekso unary operator: Kleene star - X1*
- te'au'u
- mekso ternary operator: Knuth up-arrow notation: a \uparrow \dots \uparrow b of order/with c-2 arrows ("\uparrow") initially, evaluated from right to left; the cth hyperoperator on a by b.
- te'i'ai
- 6-ary mekso/mathematical operator: Heaviside function/step/Theta function of a, of order b, in structure c, using distribution d, within approximated limit e, with value f_b at 0
- tei'au
- 4-ary mekso operator: Taylor expansion/polynomial term; for ordered input (X
_{1, X}, output is the X_{3}th Taylor polynomial term of at-least-X_{3}-smooth function X_{2}which was expanded around point X_{4}and which is evaluated at point X_{1}, namely (1/(X_{3!)) × (D^X}. - te'o'a
- unary mekso operator: natural exponentiation operator exp, where exp(a) = e
^{a \forall a}. - te'oi'i
- mekso ordered/non-commutative n-ary operator: tensor product/exterior product (of tensors); letting "@" denote the tensor product, A
_{1}@ A_{2}@...@ A_{n }. - te'oi'oi
- terminator, mekso: terminates the listing of an ordered sequence of indices for a tensor
- va'au'au
*(exp!)* - Binary mekso operator: group-theoretic conjugation (group action): maps inputs (X
_{1, X}to X_{2^(-X}= \phi_{(X}. Default: X_{3 }= 1. - vei'e
- mekso binary operator – quotient from integer-division: sgn(X
_{1)}sgn(X_{2) ((}abs(X_{1) - (}abs(X_{1) \% X}. - vei'o
*(exp!)* - binary mekso operator: form quotient space X
_{1/X}. - vei'u
- binary mekso operator: mod(ulus)/remainder; X
_{1}\% X_{2}, \,\,\, X_{1}(mod(X_{2})). - vi'oi'au
- mekso unary operator: the set of all fixed points of function a
- xa'ai
- mekso operator: the bth branch of the (possibly multivalued) function a
- xa'ei'o
- binary mekso operator: Let the inputs X
_{1}and X_{2}be sets in the same universal set O; then the result of this operator applied to them is X_{1^c \cup X}, where for any A \subseteq O, A^{c }= O \setminus A. - xa'ei'u
- binary mekso operator: Let the inputs X
_{1}and X_{2}be sets in the same universal set O; then the result of this operator applied to them is X_{1^c \cap X}, where for any A \subseteq O, A^{c }= O \setminus A. - xau'e'o
- mekso convention default specification/definition (explicit)
- xau'o'o
- mekso convention cancellation
- xe'au
- mekso clausal referent bracket initializer
- xi'ei
- binary mekso operator: for ordered list X
_{1}, this word outputs the same ordered list except the indices/subscripts have been relabelled/redefined/reindexed according to rule X_{2}(see notes). - xo'ei
- unary mekso operator: produces a string of n consecutive "xo'e"'s, treated as digits (concatenated into a single string of digits)
- xo'e'o'ei
- At-most-unary mekso operator: like {xo'ei} but for selma'o XOhEhOhE, rather than just PA
- xoi'u
*(exp!)* - non-logical connective (mekso set operator): regardless
- za'ei
- mekso binary operator: right-handed vectorial cross product (ordered input), a×b
- ze'ai'au
- unary mekso operator: reverse ordered list/tuple X
_{1}. - zei'i'au
*(exp!)* - unary mekso operator: (analytically continued) Riemann zeta function zeta(z), for complex-valued input z.
- zoi'ai
- non-mekso quote/name substitution for ordered collection of prescriptions, descriptions, definitions, etc.
- zu'oi
- mekso; binary operator: z-score for the X
_{1}quantile; X_{2}(default: 1) acts as the descriptor toggle (see notes). - cia'o'e
- mekso 4-nary operator: spherical harmonics on colatitudinal/polar angle a and azimuthal/longitudinal angle b of unassociated order c and associated order d.
- xua'ai
- mekso operator: the bth branch of the (possibly multivalued) function a

- cmaci
- x
_{1}is a mathematics of type/describing x_{2}. - dilcu
- x
_{1}is a quotient of 'x_{2}/x_{3}' [dividend x_{2}divided by divisor x_{3}], leaving remainder x_{4}. - fancu
- x
_{1}is a function/single-valued mapping from domain x_{2}to range x_{3}defined by expression/rule x_{4}. - frinu
- x
_{1}is a fraction, with numerator x_{2}, denominator x_{3}(x_{2}/x_{3}). - jalge
- x
_{1}(action/event/state) is a result/outcome/conclusion of antecedent x_{2}(event/state/process). - namcu
- x
_{1}(li) is a number/quantifier/digit/value/figure (noun); refers to the value and not the symbol. - parbi
- x
_{1}(me'o, fraction) is a ratio/rate of x_{2}(quantity) with respect to x_{3}(quantity), [x_{2}:x_{3}]. - pilji
- x
_{1}is the product/total/result of factors/multiplicands (x_{2}and x_{3}) x_{2}multiplied by x_{3}. - brima'o
- x
_{1}=c_{1}(zo) is a cmavo with a predicate role or semantic structure which expresses predicate x_{2}=b_{1}(quote/du'u) between arguments x_{3}=b_{3}(ordered list), the said cmavo being of form or in category/class x_{4}=c_{2}in/and belonging to language/dialect x_{5}=c_{3}. - sapna'u
- x1 is a scalar in structure/set x2 with properties (potentially including magnitude, etc. in a given metric and coordinate system) x3; x1 is a simple number; x1 is a number that lacks
- kurti
- x
_{1}(proposition) is data/information being an example of deep formalization of subject x_{2}gathered by method x_{3}(proposition) - bu'o'e
*(exp!)* - elliptical/unspecified/vague letteral/symbol
- cu'oi'e
*(exp!)* - convert number to statistical odds selbri; event x
_{1}(nu) has statistical odds (n) of occurring (versus not occuring) under conditions x_{2}. - ju'au
- semi-mathematical binary operator: named number base operator/interpreter
- la'e'au
- the specific referent of [following sumti] defined/specified by the grammar
- ni'ai
- x
_{1}is a number/value such that the abstraction is true, under mathematical system x_{2}; x_{1}binds to ke'a within the abstraction - noi'a'u
- PA nonrestrictive/incidental relative clause; attaches to a PA number/numeral/digit with the ke'a referring to that PA number/numeral/digit.
- poi'a'u
- PA restrictive relative clause; attaches to a PA number/numeral/digit with the ke'a referring to that PA number/numeral/digit.
- ra'ei
*(exp!)* - semi-discursive: and so forth, and so on, et cetera, continuing similarly
- xau'e
- symbol string to number/variable
- xau'o
*(exp!)* - text to number/variable
- xo'au
- pro-numeral: the most-recently mentioned full/complete numerical or mathematical string/expression.
- zau'e'u
- text affirmation/negation mode toggle
- zoi'o'e
- elliptical/unspecified/vague string/text/word
- cpolinomi'a
- x
_{1}is a formal polynomial with coefficients x2 (ordered list) of degree x_{3}(li; nonnegative integer) over structure/ring x_{4}(to which coefficients x_{2}all belong) and in indeterminant x_{5}. - enfa
- x
_{1}abstractly pertains to an exponential/root/logarithmic relationship between the elements of x_{2}(ordered pair) which are related via concrete relationship x_{3}. - fancuvitno
- x
_{1}is a fixed point of function x_{2} - kleivmu
- x
_{1}(set) is the relative set complement of x_{2}(set) in/from/with respect to/relative to set x_{3}(set; default: the relevant universal set).