** Battle of Sedan ( 1870 ), 2 September 1870

** Sigfrid Edström, Swedish sports official ( b. 1870 )

** George Albert Smith, president of The Church of Jesus Christ of Latter-day Saints ( b. 1870 )

** Gustavus M. Blech, German-American physician and surgeon ( b. 1870 )

** Andrew Brown, Scottish soccer coach ( b. 1870 )

** Dirk Jan de Geer, Prime Minister of the Netherlands ( b. 1870 )

** Rosa Luxemburg, German communist politician ( b. 1870 )

** Saki, British writer ( b. 1870 )

** Maxfield Parrish, American artist ( b. 1870 )

** Marcus Loew, Theater chain founder ( b. 1870 )

** Patrick MacDowell, an Irish sculptor ( d. 1870 )

** Horace Austin ( 1870 – 1874 )

** Alexander Stirling Calder ( 1870 – 1945 ), American sculptor, father of:

** William Hume Blake ( 1809 – 1870 ), Canadian jurist and politician

** 6 December 1928 – 1931 Sir John Robert Chancellor ( 1870 – 1952 )

** Alfred Remy, American philologist & music writer ( born 1870 )

** Dallas Lore Sharp, American nature writer ( born 1870 )

** Biographical sketch by Karl Bartsch in Franz Pfeiffer, ed., Uhlands Briefwechsel mit Freiherrn von Lassberg ( 1870 )

** Grand Duchess Alexandra Georgievna of Russia, Princess Alexandra of Greece and Denmark, ( 1870 – 1891 ), daughter of George I of Greece ; wife of Grand Duke Paul Alexandrovich of Russia as Grand Duchess Alexandra Georgievna of Russia

** Principles of Psychology ( 1870, 1880 ), in two volumes

** Military Secretary's Department ( 1870 – 1964 )

** J. Grossmann, Des Grafen Ernst von Mansfeld letzte Pläne und Thaten ( Breslau, 1870 )

** Chauncey Edgar Snow ( born 8 July 1870 )

** Alexander William Charles Oliphant Murray, 1st Baron Murray of Elibank ( 1870 – 1920 )

** Eunectes murinus, the green anaconda, the largest species, is found east of the Andes in Colombia, Venezuela, the Guianas, Ecuador, Peru, Bolivia, Brazil and on the island of Trinidad.

** Eunectes notaeus, the yellow anaconda, a smaller species, is found in eastern Bolivia, southern Brazil, Paraguay and northeastern Argentina.

** Eunectes deschauenseei, the dark-spotted anaconda, is a rare species found in northeastern Brazil and coastal French Guiana.

** Eunectes beniensis, the Bolivian anaconda, the most recently defined species, is found in the Departments of Beni and Pando in Bolivia.

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

** The Cartesian product of any family of nonempty sets is nonempty.

** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.

** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

** For every non-empty set S there is a binary operation defined on S that makes it a group.

** Tychonoff's theorem stating that every product of compact topological spaces is compact.

** In the product topology, the closure of a product of subsets is equal to the product of the closures.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

** Any union of countably many countable sets is itself countable.

** If the set A is infinite, then there exists an injection from the natural numbers N to A ( see Dedekind infinite ).

** Every infinite game in which is a Borel subset of Baire space is determined.

** The Vitali theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.

** The Lebesgue measure of a countable disjoint union of measurable sets is equal to the sum of the measures of the individual sets.

** The Nielsen – Schreier theorem, that every subgroup of a free group is free.