# Tag Info

4

As best as I can tell, the term Potenzbegriff (powerclass, later variation Potenzmenge, powerset) was introduced by Bernstein in the late 1890s (Cantor did not use it in his papers). In his Habilitation dissertation Untersuchungen aus der Mengenlehre (1901, published 1905) he states in the introduction (my translation): "The introduction of the concept of ...

5

When introducing the older terminology in the previous sentence, Peano describes it thus: ... signifie "il y a des a", "les a existent"... It seems likely this is the source of the inverted "E".

6

The real etymology is lost, I am afraid, but various speculations have been offered since antiquity and continue to this day. In Egypt the tree was known since at least 2600 BC. Egyptians already used the same name ('Bennu') for the bird and the date fruits. Bircher in The Date Palm A boon For Mankind speculates as to the reason: "This bird was found on ...

42

The short answer is that this is how he referred to himself. He was born Tyge Otteson Brahe but at the age of 15 (1561) changed 'Tyge' to Latinized 'Tycho', see Redd's biography of Tycho and Thoren's book Lord of Uraniborg. Johannes Müller, a well-known German astronomer, wrote under 'Regio Monte', which Melanchton, an educational authority at the Copenhagen ...

3

The cyrillic letter Ш (sha)is -- for obvious reasons when looking at the graph) also used to denote the "function" (well, it is a distribution if you want to be picky) given by the sum of integral displacements of the Dirac-delta function, see https://en.wikipedia.org/wiki/Dirac_comb

10

It is sometimes asserted that $\varnothing$ for the empty set was introduced by Bourbaki using a Danish and Norwegian letter. EDIT: The source is the Weil autobiography, cited in Jeff Miller's collection of the origins of mathematical expressions: André Weil (1906-1998) says in his autobiography that he was responsible for the symbol: Wisely, ...

16

The letter Ш (sha) of the Cyrillic alphabet is widely accepted in theoretical computer science as the symbol for the shuffle product, which gives the shuffle algebra. The same letter is also used to denote the Tate-Shafarevich group, but I'm not sure if it's really a standard (the letter was introduced by Cassels only in 1990 in 1962 instead of TS, see below ...

9

There are several non-alphabetic symbols, the best known is the integral sign $\int$ and the Weierstrass $P$-function $\wp$. To be sure their origins are letters of Latin alphabet, but they are special stylized symbols, and as far as I know there is no computer code for them in the standard sets of computer characters. Strictly speaking they do not belong to ...

4

Yes, orthogonal matrices with complex entries appeared at least as early as 1900, in E. Cartan's classification of simple Lie algebras (and Lie groups). In many ways, the complex numbers could be replaced by any algebraically closed field of characteristic $0$. Thinking of complex orthogonal groups as real Lie groups ("forgetting" the complex structure) ...

4

They did. A natural way to treat such matrices is to introduce an indefinite inner product on $\mathbb{C}^n$, a non-degenerate bilinear form $(z,w):=z_1w_1+z_2w_2+\dots z_nw_n$, instead of the usual sesquilinear one. Then $A^T=A^{-1}$ is equivalent to $(Az,Aw)=(z,w)$, i.e. complex orthogonal matrices are isometries of this space. The "orthogonal"/"unitary" ...

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