Mathematics HTML Sampler

• Check Widely 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 page Special Symbols (Not Widely Supported), then we have to create new graphics. • All standalone letters used as symbols should be in italic. For italics, you can use either … or …. The former are preferred, but the latter are acceptable.

Mathematical symbols with subscripts or superscripts that are also letters can be formatted using either separate tags for each italicized letter or, if there are no intervening characters that shouldn't be italicized, using a global pair 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 bibliographies for 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 font cmsy10.ttf, if it is installed, and failing that it will call for Script 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 above italic 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 a formula with x and y free, and let û represent variables u₁,…,u_k, which may or may not be free in φ. Furthermore, let φ_x,y,û[s,r,û] be the result of substituting s and r for x and y, respectively, in φ(x,y,û). Then every instance of the 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 mathematical expression, 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 complex numerators/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 the following to look good in Firefox, then the long division lines will rise up 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 with conditions, we use a table with one row per part and construct the brace out of unicode curly-brace drawing symbols. NOTE: the brace should be in its own mini-table and needs only style="line-height:1.0":

Z(h, e|k) =

⎧
⎪
⎪
⎨
⎪
⎪
⎩

P(h|e ∧ k)−P(h|k)

1−P(h|k)

if P(h|e ∧ k) ≥ P(h|k)

P(h|e ∧ k)−P(h|k)

P(h|k)

if P(h|e ∧ k) < P(h|k)

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

<td align="center">
n 
Π 
k=1
</td>

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

n
Π
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 been altered:

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 inline context (where you cannot use a table), use a nested pair of span tags with the superscript first, in the outer (“supsub”) span tag 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 code will be repeated within this paragraph to show the inline usage of the superscript over subscript. Here is the repeat of the code: Π10. This shows 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 around each 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 the default 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 entry on definitions needed both numbered equations and non-numbered equations with the same amount of indent. This was done by using a paragraph style to control the amount of indent and a corresponding table with 0 padding and a first column that matched the width of the indent. • The following entries have lots of useful examples:

Mathematics HTML Sampler

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