Fraktur in the context of Final form

A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula or a mathematical expression. More formally, a mathematical symbol is any grapheme used in mathematical formulas and expressions. As formulas and expressions are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics.

The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. Letters are used for representing many other types of mathematical object. As the number of these types has increased, the Greek alphabet and some Hebrew letters have also come to be used. For more symbols, other typefaces are also used, mainly boldface ⁠${\displaystyle \mathbf {a,A,b,B} ,\ldots }$⁠, script typeface ${\displaystyle {\mathcal {A,B}},\ldots }$ (the lower-case script face is rarely used because of the possible confusion with the standard face), German fraktur ⁠${\displaystyle {\mathfrak {a,A,b,B}},\ldots }$⁠, and blackboard bold ⁠${\displaystyle \mathbb {N,Z,Q,R,C,H,F} _{q}}$⁠ (the other letters are rarely used in this face, or their use is unconventional). It is commonplace to use alphabets, fonts and typefaces to group symbols by type (for example, boldface is often used for vectors and uppercase for matrices).

Blackletter (sometimes black letter or black-letter), also known as Gothic script, Gothic minuscule or Gothic type, is a family of scripts used in calligraphy and typefaces.

Blackletter was used throughout Western Europe from approximately 1150 until the 17th century. It continued to be commonly used for Danish, Norwegian, and Swedish until the 1870s, Finnish until the turn of the 20th century, Estonian and Latvian until the 1930s, and for the German language until the 1940s, when Adolf Hitler officially banned it in 1941. Fraktur is a notable script of this type, and sometimes the entire group of blackletter faces is referred to as Fraktur. Blackletter is not to be confused with the Old English language, which predates blackletter by many centuries and was written in the insular script or in Futhorc runes. Along with Italic type and Roman type, blackletter served as one of the major typefaces in the history of Western typography.

Antiqua (/ænˈtiːkwə/) is a style of typeface used to mimic styles of handwriting or calligraphy common during the 15th and 16th centuries. Letters are designed to flow, and strokes connect together in a continuous fashion; in this way it is often contrasted with Fraktur-style typefaces where the individual strokes are broken apart. The two typefaces were used alongside each other in the Germanophone world, with the Antiqua–Fraktur dispute often dividing along ideological or political lines. After the mid-20th century, Fraktur fell out of favor and Antiqua-based typefaces became the official standard in Germany. (In German, the term "Antiqua" refers to serif typefaces.)

Schwabacher typefaces (pronounced [ˈʃvaːˌbaxɐ]) were a style of blackletter typefaces which evolved from Gothic Textualis (Textura) under the influence of Humanist type design in Italy during the 15th century. Schwabacher typesetting was the most common typeface in Germany, until it was replaced by Fraktur from the mid 16th century onwards. In the course of the 18th and 19th centuries (but in Germany not until 1941), Fraktur gave way in turn to Antiqua.

Wochenspruch der NSDAP (lit. 'Weekly Quotation of the Nazi Party') was a wall newspaper published by the Nazi Party between 1937 and 1944, displaying quotations, mostly from Nazi leaders. About 1,100 issues were published. Some were issued by the Reichspropagandaleitung and others by local party organizations in each Gau. Along with Nazi leaders, the posters also quoted famous Germans from history, including Ludwig van Beethoven, Carl von Clausewitz, Otto von Bismarck, and Friedrich Schiller. The posters were displayed in many public locations including town halls, restaurants, doctor's offices, offices, schools or companies. Historian Jeffrey Herf estimates that 32.5 million copies were printed in total from September 1939 to when the periodical was discontinued.

The purpose of the publication was to educate Germans about Nazi ideals and values, especially those who did not take advantage of the party's indoctrination sessions. Initially, they were often printed in Fraktur type, but this changed in later editions. Anti-Nazi diarist Friedrich Kellner noted that it was printed on high-quality paper despite shortages which necessitated rationing.

The Antiqua–Fraktur dispute was a typographical dispute in 19th- and early 20th-century Germany.

In most European countries, blackletter typefaces like the German Fraktur were displaced with the creation of the Antiqua typefaces in the 15th and 16th centuries. However, in Germany and Austria, the two styles of printing coexisted until the first half of the 20th century.

In set theory, the cardinality of the continuum is the cardinality or "size" of the set of real numbers ${\displaystyle \mathbb {R} }$, sometimes called the continuum. It is an infinite cardinal number and is denoted by ${\displaystyle {\mathbf {\mathfrak {c}}}}$ (lowercase Fraktur "c") or ${\displaystyle {\mathbf {|}}{\mathbf {\mathbb {R} }}{\mathbf {|}}.}$

The real numbers ${\displaystyle \mathbb {R} }$ are more numerous than the natural numbers ${\displaystyle \mathbb {N} }$. Moreover, ${\displaystyle \mathbb {R} }$ has the same number of elements as the power set of ${\displaystyle \mathbb {N} }$. Symbolically, if the cardinality of ${\displaystyle \mathbb {N} }$ is denoted as ${\displaystyle \aleph _{0}}$, the cardinality of the continuum is

Polonophobia, also referred to as anti-Polonism (Polish: Antypolonizm) or anti-Polish sentiment are terms for negative attitudes, prejudices, and actions against Poles as an ethnic group, Poland as their country, and their culture. These include ethnic prejudice against Poles and persons of Polish descent, other forms of discrimination, and mistreatment of Poles and the Polish diaspora.

This prejudice led to mass killings and genocide or it was used to justify atrocities both before and during World War II, most notably by the German Nazis and Ukrainian Nazis. While Soviet repressions and massacres of Polish citizens were ideologically motivated, the negative attitude of Soviet authorities to the Polish nation is well-attested.