## Ψ.1.Natural repetition

### # 1.1.Maths with make-up

at the entrance
of the heavenly circus
our garbage is a golden ticket
white clowns sing the “angelus”
and there’s a *salto mortale*
that’s not difficult after all
for ¥ou

– Franzes' poem
“The circle is close”

#### §1.1.1.Wild signs

Variables are written in lower case `a,b,c,..` and can only be replaced by numbers or by expressions reducible to numbers. The number substituted for a variable depends on the context – parameters inside an expression where `1` is the only type of number unit hold natural numbers {n≥1} larger than zero.
So when you choose to substitute a new type of number, such as pi with its infinite digital expansion, the justification for doing this will be a special number function, most likely constructed from the negative `-` unit.

A wildcard in upper case `A,..,Z` holds the place of any word (sequence of characters) allowed on that position in the expression. Note that a wildcard can often also stand in for an empty string.
Accented wildcards `X'` stand for a possible next form of word `X` after a first or intermediate selection.
Wildcard `R` (sometimes `S,T` too) is reserved to designate a row or part of a row of parameters. In the following definition for a partial row `R` with `n` non-zero parameters, the empty row is substituted when the meta-repetition #n counts n=0 parameters.

R := aki,... {aki#n aki>0} = ak+1,..,ak+n {n>0}

The incrementor `i` is repeated in the corresponding ellipsis and incremented by `1` at each repetition.
The 3-point ellipsis `...` is a wildcard for a sequence, specified by a meta-repetition statement X#Y that follows after the expression. A 2-point ellipsis `..` can be used instead, and if a meta-statement doesn't follow this classic .. relies on the imagination of the reader to continue its series (common is a minimum of one item).
We notate repeating operator signs with a superscripted ellipsis `×...` or `×..`

An equation `A=B` or `A==B` states an exact reduction step of the left expression to the right.
An expression does not contain an equality sign `=` or an equal by iteration sign `==` or an approximation sign `~` or some comparison sign `< > ≠` or substitution sign `:=` or mixed sign thereof.

The inverse unit `-` generating the negative integers `-*n` is treated in chapter 2.2, as is omega `ω`.
Inverse units are appended on the right `n-` of a number, to tell them apart from subtraction n-1.
Because we use `e` as a 5th function parameter and `i` more as an incrementing index, the classic signs e for the base of natural logarithms and i = √-1 for the square root of minus one, are written as `ê` and `î = -^2^-`
You can find more special signs in the Sign dictionary.

#### §1.1.2.Colour book

Meta-expressions are written in violet font, and backslash signs can be too.
Within higher level subexpressions such as meta-expressions and subscripts we prefer to use star operator notation (with addition as zeroth star), e.g. {tm1;≥ab} specifies the comparison a+b < tm+1; as you'd usually write it.
Deeper meta-statements – owning others and therefore resolved first – can get a deeper {{magenta}} colour.

To typify individual variables, wildcards, etc. these are subscripted as: `Sign,red,orange.;;`

To highlight an error and its consequences you sometimes find red font and the `≠` not equal sign on the line.

Old style expressions in brown font use the operators +,×,^,^^,.. and apply old school precedence.

Arrows and stars `a^...b {^#m}` `= a*...b {*#m1}` both express superpowers. The two operations will result in the same number, but the latter requires an extra star.
Operations with one or more arrows can be coloured bluish simply to highlight them, but formally this is done in a multiplicative context {0^} with countable arrows, where addition is the preceding operation `a+b` (of -1 arrows) and writing `a1` in the source is improper (use `a+1` outside of meta-expressions).
Also there's the issue of precedence. Operations with more arrows are resolved before those with less arrows (majority precedence), and then a smaller number of stars is evaluated first (apply minority precedence to stars).

• Minority star operators have `text` colour `*..` and define the operatorial bigI.
• Countable `navy` majority arrows `^.. {^#c}` can be written `^c` for bigE.
• bigA's plus operations `+..` `green` are used in the construction of bigA.
• Sometimes an expression in a deviant context` ` has the colour `kryptonite`.

To improve the readability of bracketed expressions we've painted nested entries in marine colours.

E(1,blue,F(2,azure,G(3,dolfin,H(4,aquatic))))

Different fonts give emphasis to details in the mathematical code and structure to the text as a whole. The mottos and pictures reflect on the subject matter of the forthcoming chapter from a spiritual angle.
We've provided for the headers of the subdivisions in this book to be helpful as anchors, stamped in various colours. A box will contain more advanced material, a comment is a note attached to the main text.

# Part

## Chapter

### Subchapter

#### Box

##### Comment

Paragraph `Code Sub` note <source>

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