Friendly Lojban
Chapter 18. Letters, Numbers & Math
The Lojban Alphabet: lerfu
Each letter of the Lojban alphabet has a name — a cmavo of selma'o BY. These are used to spell words, give initials, or refer to letters as objects.
Vowel letters:
| Letter | Name |
|---|---|
| a | .abu |
| e | .ebu |
| i | .ibu |
| o | .obu |
| u | .ubu |
| y | ybu |
Consonant letters follow the pattern Cy (consonant + y):
| Letter | Name | Letter | Name |
|---|---|---|---|
| b | by. | m | my. |
| c | cy. | n | ny. |
| d | dy. | p | py. |
| f | fy. | r | ry. |
| g | gy. | s | sy. |
| j | jy. | t | ty. |
| k | ky. | v | vy. |
| l | ly. | x | xy. |
| z | zy. |
Apostrophe is named .y'y. and period/pause is .denpa bu.
Spelling Words
To spell a word, list its lerfu in sequence:
zo lojban cu se lerfu ly. .obu jy. by. .abu ny. "lojban" is spelled l-o-j-b-a-n.
Letter strings can be used as sumti directly: ly. .obu jy. by. .abu ny. = "lojban" (as a string of letters).
bu is a cmavo that turns any Lojban word into its letter name:
la .alis. bu — the letter/symbol "Alice" (Alice used as a symbol) lo skami bu — the symbol "skami"
This is how arbitrary symbols and single-character names are created on the fly.
Numbers: PA cmavo
The ten digits are single cmavo:
| Digit | Lojban |
|---|---|
| 0 | no |
| 1 | pa |
| 2 | re |
| 3 | ci |
| 4 | vo |
| 5 | mu |
| 6 | xa |
| 7 | ze |
| 8 | bi |
| 9 | so |
Numbers are written by concatenating digits left-to-right (most significant first):
parebici = 1283 rezevomu = 2745
Two-digit values work the same way: pa no = 10, pa pa = 11, ci mu = 35.
Special number words:
| Word | Meaning |
|---|---|
| ro | all / every |
| su'o | at least one / some |
| me'i | less than |
| za'u | more than |
| du'e | too many |
| mo'a | too few |
| rau | enough |
| piso'a | almost all |
| xo | how many? (question) |
Number Bases and Fractions
pi is the decimal point:
ci pi vo = 3.4 pamu = 0.5 (half)
Numbers as selbri (PA as brivla-like): a number alone acts as a quantifier or a predicate:
le ci gerku = the three dogs mi ci = I am three (I am the third) pa le gerku cu blabi = one of the dogs is white
fi'u = fraction separator:
pa fi'u re = 1/2 ci fi'u vo = 3/4
ma'u / ni'u = positive / negative sign:
ni'u re = −2 ma'u mu = +5
Mathematical constants (PA cmavo standing alone):
| cmavo | Value |
|---|---|
| pai | π (pi, ≈ 3.14159…) |
| te'o | e (Euler's number, ≈ 2.71828…) |
| ci'i | ∞ (infinity) |
| ci'i no | ℵ₀ (aleph-null, countable infinity) |
li pai su'i te'o = π + e
ki'o = comma separator (thousands):
pa ki'o = 1,000 re ki'o vo no no = 2,400
ce'i = percent sign (follows the number):
ci mu ce'i = 35% pamu ce'i = 50%
ka'o = imaginary-unit separator for complex numbers:
ci ka'o re = 3+2i (three plus two-i) ni'u pa ka'o vo = −1+4i
Ordinal Numbers
Place moi after a number to get an ordinal:
pamoi = first remoi = second cimoi = third
mi pamoi klama = I am the first to go. le remoi prenu = the second person
mei makes a number into "a set/group of N":
le ci mei = the trio / the group of three
Math: mekso
Lojban has a full mathematical expression system called mekso ("mathematical expression"). It is designed to be unambiguous — operator position, parentheses, and precedence are all explicit.
li — Math Expressions as Sumti
li introduces a numeric or mathematical expression as a sumti (a number-as-object):
li ci su'i vo du li ze The number (3 + 4) equals the number 7.
du = equals (mathematical identity). The whole mekso expression follows li.
Operator Order
Mekso supports two operator positions:
Infix (operator between operands) — most natural for simple expressions:
li re su'i ci = 2 + 3 = 5 li mu vu'u re = 5 − 2 = 3 li re pi'i ci = 2 × 3 = 6
Polish / forethought (operator before operands) — unambiguous for nested expressions:
li su'i re ci = +(2, 3) = 5
In practice, infix is most common for simple arithmetic. For complex nested expressions, vei…ve'o parentheses make infix equally unambiguous.
vei … ve'o — Parentheses in Mekso
vei opens a parenthesized sub-expression; ve'o closes it:
li vei re su'i ci ve'o pi'i vo du li re no (2 + 3) × 4 = 20
Without vei, bi'e, or a ti'o precedence declaration, infix VUhU operators group left to right (like a simple calculator) — not automatic “multiplication before addition” . So li re su'i ci pi'i vo means ((2 + 3) × 4) = 20, not 14.
li re su'i vei ci pi'i vo ve'o — 2 + (3 × 4) = 14
Explicit vei/ve'o stays the clearest fix; bi'e (below) is the compact alternative.
bi'e — higher-precedence operators (compact infix)
Prefix bi'e to a VUhU operator (selma'o BIhE) so that operator binds before neighbors that lack bi'e — the standard Lojban way to get “multiply before add” on one line:
li ci su'i vo bi'e pi'i mu du li reci 3 + (4 × 5) = 23
If several operators carry bi'e, grouping is from the right; bi'e bi'e on a single operator is not allowed. When a formula gets busy, prefer vei … ve'o or split across sentences.
Logical connectives within mekso
Operands and operators follow the same connective classes as ordinary language: sumti-style eks (.e, .a, …) between operands, jeks (je, ja, …) between VUhU operators (Chapter 8). A few consequences:
- Quantifiers often wrap mekso in vei … ve'o when the number is not a single PA:
vei ci .a vo ve'o prenu cu klama le zarci Three or four people go to the market.
- lo'o closes li when the next connective belongs to the outer sentence, not to the mekso:
li re su'i re du lo'o .ije … Two plus two equals …, and …
- Operators can be joined (contrived but grammatical):
li re su'i je pi'i re du li vo Two [plus and times] two equals four. (parallel to su'i je pi'i as a connected operator cluster)
CLL has full tables for operand/operator connection and for ke-grouping of operators; for textbook prose, prefer explicit vei/ve'o and separate sentences until you need this density.
Full VUhU Operator Table
VUhU operators are used in mekso (mathematical expressions). They work in infix (between operands) or in Polish/forethought notation (before operands).
| cmavo | Operation | Arity | Example |
|---|---|---|---|
| su'i | addition (+) | binary | re su'i ci = 5 |
| vu'u | subtraction (−) | binary | mu vu'u re = 3 |
| pi'i | multiplication (×) | binary | re pi'i ci = 6 |
| fe'i | division (÷) | binary | xa fe'i re = 3 |
| te'a | exponentiation (^) | binary | re te'a ci = 8 |
| ne'o | factorial (n!) | unary, postfix | mu ne'o = 120 |
| de'o | logarithm (log_b of n) | binary | de'o re boi bi = log₂(8) = 3 |
| fe'a | root (n-th root of m) | binary | fe'a re boi bi = √8 ≈ 2.83 |
| ge'a | absolute value ( | n | ) |
| gei | scientific notation (× 10^n) | binary | ci gei bi = 3 × 10⁸ |
| pi'a | vector/matrix row joining | binary | constructs vectors |
| sa'i | matrix column joining | binary | constructs matrices |
| fu'u | n-ary operation (unspecified) | n-ary | general placeholder |
| sa'o | derivative operator | unary/binary | calculus |
| ji'i (PA) | approximately equal to | (quantifier in number context) |
Unary operators take one operand; binary take two. When used as VUhU in Polish notation, the operand count must be satisfied: su'i re ci = +(2,3) = 5 (binary, both operands follow).
The boi separator distinguishes multiple operands when two numbers would otherwise run together:
de'o re boi bi = log base 2 of 8 (boi separates the base "re" from the argument "bi")
Special Number Words in Detail
Beyond simple digits, the PA cmavo include several "fuzzy" quantity words:
| cmavo | Meaning |
|---|---|
| ro | all / every |
| su'o | at least one / some (existential) |
| su'e | at most N |
| su'o re | at least two |
| du'e | too many |
| mo'a | too few |
| rau | enough |
| za'u | more than N |
| me'i | fewer/less than N |
| ji'i | approximately / roughly N |
| piso'a | almost all |
| piro | all of (used with masses) |
| xo | how many? (question) |
ji'i panono prenu pu klama Approximately 100 people came.
za'u re nanmu cu zvati More than two men are present.
me'o introduces a numeral as a symbol (not evaluated as a quantity):
me'o xy. = the symbol x (as a variable name, not a number) me'o paremubi = the string "1-2-8" as a symbolic label
na'u and ni'e: Connecting Mekso with Selbri
na'u converts a VUhU operator into a selbri usable in a regular Lojban bridi. The resulting selbri has the place structure of the underlying mathematical relation.
Worked example — na'u su'i (addition as selbri):
The VUhU su'i (addition) has the implicit place structure:
- x₁ = the sum
- x₂ = one addend
- x₃ = the other addend
When promoted to selbri via na'u:
li mu na'u su'i re ci 5 is the sum of 2 and 3. Literally: 5 [is-x₁-of addition] 2 3
li re na'u su'i ci du li mu 2 + 3 = 5 (using du = "equals" to close the equation)
You can use SE conversion on na'u-selbri:
li re na'u se su'i mu 2 is an addend summing to 5 (se shifts x₁↔x₂: now x₁ is an addend, x₂ is the sum)
Another example — na'u pi'i (multiplication as selbri):
li xa na'u pi'i re ci 6 is the product of 2 and 3.
la meris. cu se zmadu la .alis. lo ka barda Mary exceeds Alice in bigness. (non-mekso parallel)
The power of na'u is that it lets you make claims about mathematical relationships using the full Lojban logical and quantifier system:
ro da poi kacna'u zo'u su'o de poi kacna'u zo'u da na'u su'i de du li no For every integer, there is some integer whose sum with it equals zero. (additive inverses)
ni'e converts a selbri into a mekso operand — the selbri's x₁ determines the numeric value:
li ni'e melbi pi'i re The beauty-value times two (treating "beauty" as a numeric measure)
mo'e converts any sumti (often a ni abstraction) into a mekso operand:
li mo'e le ni le pixra cu blanu the number representing how blue the picture is
MOI: Quantifier Selbri
moi and mei turn numbers into selbri. The full MOI series:
| cmavo | x₁ is… | Example |
|---|---|---|
| moi | the Nth member of set x₂ | mi pamoi = I am first |
| mei | a group of N from x₂ | le ci mei = the group of three |
| si'e | an Nth portion / fraction of x₂ | le pimu si'e le plise = half the apple |
| cu'o | an event with probability N | le nu carvi cu pimu cu'o = 50% chance of rain |
| va'e | at level N on scale x₂ | mi ci va'e melbi = I am beauty-level 3 |
mi pamoi klama = I am the first to go. le remoi prenu = the second person. le pimu si'e le plise cu fusra = Half the apple is rotten. le nu carvi cu pano cu'o = There is a 10% probability of rain. do vo va'e certu = You are a level-4 expert.
Subscripts: xi
xi attaches a subscript (a number or letter string) to almost any word:
ko'a xi pa = ko'a₁; ko'a xi re = ko'a₂ fa xi xa = the 6th place tag (extending beyond the standard fa/fe/fi/fo/fu) da xi vo = x₄ (logical variable with subscript)
Subscripts allow infinite extension of any finite cmavo series. They are particularly useful for:
- Extending logical variables: da xi pa, da xi re, da xi ci = x₁, x₂, x₃
- Tracking multiple discourse referents: ko'a xi pa = "the first one", ko'a xi re = "the second one"
- Math variables: xy. xi pa = x₁ (the symbol x subscript 1)
Spelling and Letterals in Depth
bu: The Universal Letter-Maker
bu following any Lojban word converts it to a lerfu (a letter or symbol) representing that word:
zo coi bu = the symbol "coi" (the word coi treated as a single glyph/symbol) la bu = the symbol "la" mi bu = the symbol "mi" (useful for algebra-like notation)
This lets you create symbols for any concept on the fly.
Letterals as Pro-Sumti
Outside math contexts, lerfu strings (like .abu, xy.) act as a second set of assignable pronouns alongside ko'a…ko'u:
.abu cu klama — .abu goes (tracking a referent) xy. du li re — x = 2 (math variable) da xi pa zo'u xy. xi pa du da xi pa — x₁ = da₁ (linking symbolic to logical)
This extends the Lojban pronoun system almost without limit.
Upper and Lower Case: ga'e, to'a, tau
Lojban does not capitalize sentences or names. Capital letters only appear inside Lojbanized names to mark irregular stress (e.g., .iVAN.). To spell out names with capital letters, use the shift words:
| cmavo | selma'o | Effect |
|---|---|---|
| ga'e | BY | shift following letterals to UPPER CASE |
| to'a | BY | shift back to lower case |
| tau | LAU | shift only the immediately following letteral to upper case (single-shift) |
ga'e and to'a are persistent — they stay in effect until contradicted:
.ibu ga'e vy. .abu ny. to'a i V A N (the name "Ivan" with Russian capitals)
tau shifts only one letter, then reverts. Useful for chemical element symbols:
tau sy. = S (upper-case S = sulfur symbol) tau sy. .ibu = Si (silicon: upper S then lower i)
If a global upper-case shift (ga'e) is active, tau reverses it for that one letter (producing lower case).
Compound Letterals: tei … foi
tei and foi create a compound lerfu — multiple letters treated as a single, indivisible symbol:
tei xy. ny. foi = the compound symbol "xn" (treated as one unit) tei .abu xy. foi = the symbol "ax"
This is needed when a lerfu string should be interpreted as a single symbol rather than separate letters in sequence. Useful for creating multi-character variable names.
tei/foi are also essential for accent marks in foreign words. Accent marks have their own lerfu words, but the ordering (mark before or after the base letter?) is language-specific. tei…foi removes the ambiguity by grouping base + mark into one unit:
tei .ebu .akut.bu foi ty. tei .akut.bu .ebu foi (é) t (é) — spells French été unambiguously
The acute accent is .akut.bu (the name akut. + bu). It doesn't matter whether it comes before or after .ebu inside the tei…foi brackets — the grouping guarantees association.
Similarly, tei handles multi-letter digraphs that some languages treat as single letters:
tei ly. ly. foi = the Spanish ll (a single letter in traditional Spanish)
me'o: Referring to the Letter Itself
When a lerfu string appears in running Lojban text, it acts as a pro-sumti (a pronoun — see Letterals as Pro-Sumti above). This means .abu is interpreted as "the thing previously assigned to .abu", not as a reference to the letter a.
To refer to the letter itself — to say "a is a letteral" — use me'o:
.abu cu lerfu ✗ — attempts to find a previous referent named .abu me'o .abu cu lerfu ✓ — The expression "a" is a letter.
me'o (selma'o LI) is the "mathematical expression" introducer. It signals: treat what follows as the symbol itself, not as a reference to what the symbol denotes.
me'o xy. cu se lerfu la .alis. The letter "x" is used in Alice's name.
dei vasru vo lerfu poi me'o .ebu This sentence contains four instances of the letter "e".
Contrast with quoting:
| Form | Meaning | Correct for |
|---|---|---|
| lu .abu li'u | "the word .abu" | the cmavo form |
| la'e lu .abu li'u | the referent of the word .abu | what .abu points to |
| me'o .abu | the letter a | the lerfu itself |
Spelling Words Aloud
To spell a word letter by letter:
la .alis. cu se lerfu .abu ly. .ibu sy. "Alice" is spelled a-l-i-s. (simplified spelling)
To assemble letters back into a word, use lu'o (mass of) to collect the lerfu into a single word-object:
lu'o .aby ly .ibu sy. du zo alis a+l+i+s = "alis" (the mass of these letters equals the word alis)
Quoting Rafsi and Non-Words
lo'u…le'u quotes non-grammatical strings. For rafsi and morphological fragments:
lo'u kla le'u = the rafsi "kla" (for klama) lo'u -alis- le'u = the fragment "-alis-" as a string
Counting and Measurement
la'u + number = measurement tag (how much):
la'u li mu = for a quantity of five / by fives
Comparisons are clearest with zmadu / mleca and a ka property (see Chapter 14); mau / me'a as BAI tags often want se conversion in real text.
mi zmadu do le ka barda I am bigger than you.
le zarci cu mleca le zdani le ka barda The store is smaller than the house (in size).
Forethought Operators: Polish Notation in mekso
Standard mekso uses infix operators (between operands). Lojban also supports forethought (Polish notation) where the operator comes first, before its operands. This is marked by pe'o:
pe'o su'i ci vo = +(3, 4) = 7
li pe'o su'i ci vo du li ze 3 + 4 = 7 (Polish form)
Forethought is more explicit and unambiguous because the operator comes first and the operands follow in order. It's closer to function notation:
pe'o pi'i re ci vo = ×(2, 3, 4) = 24 (three-argument multiplication)
The ku'e terminator closes a forethought expression when there could be ambiguity about how many operands were taken.
Forethought in complex expressions:
pe'o su'i pe'o pi'i re ci pe'o pi'i vo mu = +(×(2,3), ×(4,5)) = 6 + 20 = 26
No parentheses needed — the nesting is unambiguous because each pe'o expression takes exactly as many operands as the operator requires.
Non-Decimal Bases
By default, Lojban numbers are base 10. To express a numeral string in another base, use the VUhU operator ju'u between the number-in-that-base and the base (see the Bases section in this chapter above for full detail). Digits pa through so still mean 1–9; bases above 10 use extra digit cmavo (dau, fei, …).
li panopano ju'u re du li pano The number [written] 1010 in base 2 equals [decimal] 10.
li daufeigai ju'u paxa du li rezevobi The number [written] ABC in base 16 equals [decimal] 2748.
Only digit values valid in the chosen base may appear on the left of ju'u (e.g. do not use re as a digit in base 2).
ra'o (selma'o RAhO) flags a GOhA pro-bridi so that pro-assignments inside the copied bridi are updated for the new context — the standard device for “viewpoint shift” in indirect speech, not a general pronoun reset (use da'o for assignable sumti).
Reverse Polish Notation
Besides prefix (forethought) and infix, mekso also supports postfix (Reverse Polish Notation / RPN), common in HP calculators and Forth:
fu'a (selma'o FUhA) marks the start of an RPN expression.
fu'a ci vo su'i = 3 4 + (the operator comes after both operands) = 7
fu'a re ci pi'i vo su'i = 2 3 × 4 + = (2×3)+4 = 10
RPN is unambiguous without parentheses when operator arity is known. It's rarely used in everyday Lojban but is provided for completeness (and for stack-machine enthusiasts).
Mekso: vectors, indefinite numbers, precedence, and word problems
This block lines up with places where the preceding sections have been lighter: arrays, fuzzy counts, formal precedence, and a worked “story problem.”
Vectors and matrices: jo'i, pi'a, sa'i
A vector is a fixed list of simple operands. jo'i (selma'o JOhI) opens the list; boi separates components; te'u closes (often elidable when unambiguous):
li jo'i paboi reboi te'u su'i jo'i ciboi voboi te'u du li jo'i voboi xaboi te'u (1, 2) + (3, 4) = (4, 6).
pi'a stacks row-vectors into a matrix; sa'i stacks column-vectors. Extra rows/columns chain with the same operator (CLL uses ge'a between operands when needed). A compact 2×2:
li jo'i paboi reboi pi'a jo'i ciboi voboi The matrix with rows (1, 2) and (3, 4).
The classic 3×3 “magic square” from CLL is built the same way with three jo'i … operands joined by pi'a (or three columns joined by sa'i). When you combine matrices with other operators, wrap in vei … ve'o so grouping stays obvious.
Indefinite PA (and roi)
Besides ji'i, za'u, me'i, su'e, su'o (already above), Lojban has so'a, so'e, so'i, so'o, so'u — five objective indefinite sizes below ro, in decreasing order (roughly: almost all → … → a few). They are still vague: so'e is not “more than half” by rule.
pi-prefixed forms (piro, piso'a, …) talk about parts of a whole (masses), not “N items out of a bag.” no'o is “the typical amount” (not necessarily a statistical mean — see CLL).
Those cmavo usually quantify sumti. Inside li, prefer explicit arithmetic, ji'i, or bounds (su'o re … su'e mu) when you need a numeric claim with slack.
Digit + roi is not a mekso operator: it builds tenses like English once, twice (e.g. pare roi, reroi) — see Chapter 9 and Chapter 21 for samples.
Explicit operator precedence (ti'o)
CLL describes ti'o (with sei-family syntax) as a place to declare relative precedence among VUhU operators for future parsers. Current practice: default infix is left-to-right (see bi'e under Operator Order); spell school-math grouping with vei … ve'o or bi'e, or use forethought pe'o / fu'a. Do not assume readers apply “PEMDAS” unless you mark it.
nu'a — operator into selbri (inverse of na'u)
nu'a wraps a VUhU cmavo as an ordinary selbri (inverse of na'u). One CLL-style illustration:
li ni'umu cu nu'a va'a li ma'umu −5 is the negation-as-operation applied to +5.
Together, na'u and nu'a let you answer “which operator?” questions without a dedicated operator-question cmavo (CLL §18.19).
“Four score and seven” — the number 87
A score is 20 (like a dozen is 12). Four score and seven = 87. Several honest Lojban renderings:
li bize — plain 87 (correct, dry).
li vo pi'i reno su'i ze — four times twenty, plus seven.
li vo pi'e ze ju'u reno — digit string “4;7” read in base 20 (French quatre-vingt-sept flavor).
CLL also discusses mo'e with mei-style sumti (voboi renomei, “four twentysomes”) to mimic “four groups of twenty” before adding seven; the same pattern works in this chapter — te'u closes the mo'e expression when needed; see the Sumti as operands section above.
mai and mo'o — “firstly…”, section numbers
mai (selma'o MAI) turns a digit string or lerfu string into a free modifier: an outline label like English firstly, secondly, nth, or lastly.
pamai — firstly remai — secondly romai — lastly (literally “all-thly”)
ny.mai — nth (after ny. as “n”)
mo'o is the same idea for larger chunks of structure: chapters vs paragraphs, acts vs scenes. A pasomo'o line marks a high-level slice; inside it you might still use pamai / remai for steps. Full discussion of moʻo in text structure is in Chapter 17.
Grammar note: there is no boi between the number/lerfu string and mai / roi (same rule family) — see the mai / mo'o section above in this chapter.
bu in Depth: Any Word as a Symbol
bu is not just for common letters — it converts any Lojban word into a symbol name. This makes it possible to use arbitrary words as single-character labels:
klama bu = the symbol "klama" (the word treated as a single letter/symbol) la .teris. bu = the symbol "T" (using the name Terry as a symbol) lo gerku bu = the symbol "dog" (used as a label)
This extends to create symbols for mathematical or logical variables using recognizable Lojban words:
prenu bu = p (person symbol) gerku bu = g (dog symbol)
And for single punctuation characters or other signs:
lidne bu = a leading-dot symbol .y'y. = the apostrophe letter name (already built in) denpa bu = the period / pause mark (already built in)
bu is also how you refer to non-Lojban scripts: you can create lerfu words for Greek letters (alfas., betas., etc. using cmene convention), Cyrillic, Hebrew, and others, by combining bu with borrowed names.
Acronyms, character codes, punctuation, and script shifts
Acronyms (initials as names): Glue lerfu words into a cmene: insert ' wherever two vowels would touch, and end with a consonant (often repeating the last lerfu’s consonant or tagging culture: merko, brito, …). Compression: vowel lerfu may drop bu except .y.bu. Alternative: treat the string as a predicate-name with la me:
la me dy. ny. .abu That which satisfies “d, n, a” — usable as a name DNA-style, with pauses allowed between lerfu.
se'e (BY) — computerized codes: se'e + a PA number is one character in an agreed charset (ASCII, Unicode hex with a spoken convention, …). The hearer must know the table and base.
me'o se'e cixa cu lerfu la .asycy'i'is. The expression “code 36” is a letteral in ASCII. (36 = dollar sign in ASCII)
Unicode (hex) and “big” scripts: The same se'e device works for Unicode when everyone agrees you are using hexadecimal code points and the Unicode chart — not just ASCII. For Unicode code points, spell them as digit strings with se'e acting as a base-16 prefix; for example, U+262E (peace symbol ☮) is me'o se'e rexarerei (hex digits r·e·x·a·r·e·r·e·i under the BY names: re=2, xe=6, reno=2, bi=E). For CJK or any long non-Latin passage, zoi / la'o (Chapter 17) is usually clearer than spelling glyph-by-glyph; zai + an alphabet name still switches BY strings when you need a short native letter inside Lojban prose (see zai / ce'a below in this section).
lau (LAU) — punctuation, not letters: lau must be followed by a BY word. It marks that the bu-symbol names a punctuation mark (comma, dash, …), not an alphabetic letter — important when the same shape could be read either way.
zai (LAU) / ce'a (LAU) — shifts: zai switches which alphabet following BY words belong to (Latin vs Greek, …) until cancelled. ce'a switches font or glyph style (italic, bold, …). Interpretation depends on agreed conventions.
Raw foreign text: For un-Lojbanized passages, use zoi / la'o (Chapter 17 — Text Structure & Quotation). Tone digits in pinyin-style spellings can sit inside lerfu strings: .abu ny. vo … = han⁴….
Auxiliary lerfu cmavo (roadmap): tei/foi (compound glyph); ga'e/to'a/tau (case); lau/zai/ce'a (punctuation / alphabet / font); se'e (code point); me'o/lo'o (quote expression / close li). Not every CLL corner case is needed until you typeset mixed scripts or data protocols.
Summary
Lerfu (letters):
- Vowels: .abu .ebu .ibu .obu .ubu ybu
- Consonants: by. cy. dy. etc.
- bu turns any word into a letter/symbol name — extends to any alphabet
- tei … foi = compound multi-character symbol (also used to group base letter + accent mark)
- se'e + PA = numeric character code (ASCII/Unicode by convention — see Unicode paragraph under Acronyms…); lau/zai/ce'a = punctuation / alphabet / font shifts on BY
- Acronyms: glue lerfu into cmene, or la me + lerfu string
- Lerfu strings outside math act as assignable pro-sumti
Case shifts:
- ga'e = shift all following lerfu to UPPER CASE (persistent until to'a)
- to'a = shift back to lower case
- tau (LAU) = single-shift: next lerfu only to upper case (or lower if ga'e active)
- Example: .ibu ga'e vy. .abu ny. to'a = i V A N
Accent marks:
- Accent marks are lerfu words (e.g. .akut.bu = acute accent)
- Use tei…foi to bind accent to its base letter unambiguously regardless of order
- tei .ebu .akut.bu foi = é (e with acute) — order within tei/foi doesn’t matter
me’o — referring to the letter itself:
- Bare lerfu strings (.abu, xy.) are pro-sumti (pronouns), not references to the letter
- me’o .abu = the letter a itself (selma’o LI; treats what follows as a symbolic expression)
- Contrast: lu .abu li’u = the word “.abu”; la’e lu .abu li’u = the referent of .abu; me’o .abu = the letter a
Numbers (PA):
- Digits: no pa re ci vo mu xa ze bi so (0–9)
- Concatenate for multi-digit: parebici = 1283
- pi = decimal point; fi'u = fraction; ni'u/ma'u = sign
- Fuzzy quantities: ji'i (approx), za'u (more than), me'i (less than), du'e (too many)
Ordinals/cardinals/fractions:
- pamoi, remoi = 1st, 2nd; pa mei = group of one
- pimu si'e = half-portion; pimu cu'o = 50% probability; ci va'e = level-3
Math (mekso):
- li = introduces a number/expression as sumti
- Logical connectives inside mekso: eks between operands, jeks between operators (Ch.8); lo'o closes li before an outer .ije (etc.)
- me'o = introduces a numeral as a symbolic label (not evaluated)
- su'i, vu'u, pi'i, fe'i, te'a = +, −, ×, ÷, ^
- ne'o = factorial; de'o = log; ge'a = absolute value; gei = scientific notation
- jo'i … te'u = vector; pi'a / sa'i = matrix from row / column vectors
- vei … ve'o = mekso parentheses
- bi'e = precedence bump on an infix VUhU (multiply-before-add style); default infix is left-to-right, not PEMDAS — see bi'e under Operator Order
- boi = operand separator
- du = mathematical equals; xi = subscript
- na'u / nu'a = operator ↔ selbri (inverse cmavo pair); ni'e = selbri → operand; mo'e = sumti → operand
- mai / mo'o = outline labels (firstly, big section numbers); see mai / mo'o under Mekso: vectors…; discourse detail in Chapter 17
- ti'o = planned precedence declarations for future parsers — meanwhile use vei/ve'o, bi'e, or forethought; default infix is left-to-right, not PEMDAS
- Indefinite PA: so'a … so'u (ordered fuzzy sizes); pi-forms for fractions of masses; roi after digits = tense, not math (Ch.9)
- pe'o = forethought (Polish) notation: operator comes first
- fu'a = reverse Polish (postfix) notation: operator comes last
- ju'u = base specifier for non-decimal numbers