Mathematics HTML Sampler

• CheckWidely Supported HTML and Unicode Characters, to see whether the symbol you might need is there. If not, and it also can't be found on the pageSpecial Symbols (Not Widely Supported), then we have to create new graphics.• All standalone letters used as symbols should be in italic. Foritalics, you can use either … or…. The former are preferred, but the latterare acceptable.

Mathematical symbols with subscripts or superscripts that arealso letters can be formattedusing either separate tags for each italicized letter or, if there areno intervening characters that shouldn't be italicized, using a globalpair of … tags. So,

x_i

can be formatted as either

xi

xi

• Parenthesis should not be in italics:

∀x(Fx →Gx), i.e., ∀x(Fx → Gx),

but not

∀x(Fx → Gx), i.e., not ∀x(Fx → Gx)

Quantifiers should not use dot notation:

∀x(Fx →Gx)

not

∀x.Fx →Gx

• To stop a linebreak, place the material in the following environment:

• To produce numbered equations, use:

<dl class="hangindent">
<dt>(#)</dt><dd>equation</dd></dl>

to produce

(#): equation

or if you don't want the numbers indented, use "hang" instead of"hangindent" to produce

(#): equation

Note that the dl "hang" class can also be used in bibliographiesfor primary sources organized by year or abbreviation.

• To produce Quine corner quotes, use:

⌜some text⌝

to produce:

^⌜some text^⌝

• To produce an overbar over an uppercase letter or letters, use:

EQI

to produce:

EQI.

Note that this doesn't work as well with lower case letters:α.

• To produce a sans serif font, use

Cong

to produce

Cong

• To produce small-caps, use:

This is in small-caps

to produce:

This is in small-caps.

• To use LaTeX-like script letters for upper-case, use

…

to produce:

A,B,C,D,etc.

When the browser sees the HTML code, it will first try to call up the fontcmsy10.ttf, if it is installed, and failing that it will call forScript MT, or any "cursive" font.

• To use underbars that are lower than underlines, use

…

to produce:

A,a,B,b, etc.

• There are new span (and italic) classes, "overstrike", "up", and "hi", to put a mark above an arbitrary character. Here are some examples. Use

v&circ;
ε’

to produce:

vˆ,ε’, etc.

For upper case characters, use

U&circ;
Γ’

to produce:

Uˆ,Γ;’, etc.

To put a mark aboveitalic characters, use:

x¨
v·
etc.

to produce:

x¨,v·,a˜,gˆ, etc.

For upper case italic characters, use some combination of the above, e.g., as in

A&oline;

to produce:

A‾.

• Example of logical and se-theoretical formatting, from https://plato.stanford.edu/entries/set-theory/ZF.html:

Suppose that φ(x,y,û) is aformula withx andy free, and letûrepresent variablesu₁,…,u_k,which may or may not be free in φ. Furthermore, letφ_x,y,û[s,r,û]be the result of substitutings andr forx andy, respectively, inφ(x,y,û). Then every instance ofthe following schema is an axiom:
Replacement Schema:
∀u₁…∀u_k[∀x∃!yφ(x,y,û) → ∀w∃v∀r(r∈v ≡ ∃s(s∈w & φ_x,y,û[s,r,û]))]

• To produce a numerator/denominator in a mathematicalexpression, use:

<table style="border-spacing:0px;">
<tr>
<td style="padding:0px;border-bottom:1px solid black; text-align:center;">numerator</td>
</tr>

<tr>
<td style="padding:0px; text-align:center;">denominator</td>
</tr>
</table>

to produce

numerator
denominator

However, we may have to tweak the "padding" values to get some complexnumerators/denominators, such as the following, to look good in Firefox:

P_α[h_[q] |b·cⁿ·eⁿ]
P_α[h_[r] |b·cⁿ·eⁿ]
=
q^m (1−q)^n−m
r^m (1−r)^n−m
·
P_α[h_[q] |b]
P_α[h_[r] |b]

In the above, we increased the padding for the cell for the numerator(which has a solid black border-bottom of 1px) to 4px:

<td style="padding:4px;border-bottom:1px solid black; text-align:center;">

However, if you tweak the padding in the denominator to get thefollowing to look good in Firefox, then the long division lines will riseup above the minus sign:

1 −
1
n
·
(log γ)²
EQI[cⁿ |h_i/h_j |h_i·b] + (log ε)/n )²

• numerator/denominator with double line in between:

W[((X,Y),Z)]⇒C
W[(X,(Y,Z))]⇒C

• To produce a large left brace for an equation given withconditions, we use a table with one row per part and construct thebrace out of unicode curly-brace drawing symbols. NOTE: the braceshould be in its own mini-table and needs only:

Z(h,e|k) =
⎧
⎪
⎪
⎨
⎪
⎪
⎩

P(h|e ∧k)−P(h|k)
1−P(h|k)
ifP(h|e ∧k) ≥P(h|k)
P(h|e ∧k)−P(h|k)
P(h|k)
ifP(h|e ∧k) <P(h|k)

• To produce a summation or intersection with upper and lowerindices, use the following table parameters:

<td align="center">
n 
Π 
k=1
</td>

to produce a large product sign with a centeredindex "k=1" below and a centered index "n":

n

k=1

Note that the index class is defined with CSS

.index { font-size:.8em; line-height: 80%; }

So, if local adjustments are needed in a particular entry, the line

n

can be replaced with the following line in which the values .8em and 80% have beenaltered:

n

Thus, for integrals, we might use:

<td align="center">    ∞ 
∫ 
0</td>

to produce

∞

0

or use:

<td align="center">
     x 
∫ 
−∞
</td>

to produce

x

−∞

• To produce a superscript directly above a subscript in an inlinecontext (where you cannot use a table), use a nested pair of span tagswith the superscript first, in the outer (“supsub”) spantag and the subscript after it—within the nested(“lower”) span tag. For example,

Π10

produces

Π10

which works within the middle of a paragraph. For example, the codewill be repeated within this paragraph to show the inline usage of thesuperscript over subscript. Here is the repeat of the code:Π10. Thisshows the usage of the HTML code within a paragraph.

• To produce a thinner, blacker line than the usual <hr/> tag, use:

<hr size="2" noshade="noshade" />

to produce

• To produce a border around a table without a border aroundeach cell, use

<table style="border:1px solid black;">

to produce:

row 1, column 1 row 1, column 2
row 2, column 1 row 2, column 2

instead of of the default table border:

row 1, column 1 row 1, column 2
row 2, column 1 row 2, column 2

Additionally, to put some padding within the table border, use

<table style="border:1px solid black; border-spacing: 0.5em 1em;">

to produce:

row 1, column 1 row 1, column 2
row 2, column 1 row 2, column 2

Finally, to produce a border around every cell which is thinner than thedefault border="1", use:

<table border="1" cellspacing="0">

to produce

row 1, column 1 row 1, column 2
row 2, column 1 row 2, column 2

• An example for type-logical-grammar:

Γ,x :A ⊢M :B ⊸I
Γ ⊢ λx.M :A ⊸B
Γ ⊢M :A ⊸B Δ ⊢N :A ⊸E
Γ, Δ ⊢ (M N) :B

• The entryondefinitionsneeded both numbered equations and non-numbered equations with thesame amount of indent. This was done by using a paragraph style tocontrol the amount of indent and a corresponding table with 0 paddingand a first column that matched the width of the indent.• The following entries have lots of useful examples:

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Mathematics HTML Sampler

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