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University of Leipzig. Johannes Widmann (c. 1460 – after 1498) was a German mathematician. The + and - symbols first appeared in print in his book Mercantile Arithmetic or Behende und hüpsche Rechenung auff allen Kauffmanschafft published in Leipzig in 1489 in reference to surpluses and deficits in business problems. [1]
0810106051. OCLC. 650. The Foundations of Arithmetic (German: Die Grundlagen der Arithmetik) is a book by Gottlob Frege, published in 1884, which investigates the philosophical foundations of arithmetic. Frege refutes other idealist and materialist theories of number and develops his own platonist theory of numbers.
Dirichlet's theorem on arithmetic progressions. In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a positive integer. In other words, there are infinitely many primes that are ...
Proof without words of the arithmetic progression formulas using a rotated copy of the blocks. An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of ...
Second-order arithmetic. In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics. A precursor to second-order arithmetic that involves third-order parameters was ...
The first block is a unit block and the dashed line represents the infinite sum of the sequence, a number that it will forever approach but never touch: 2, 3/2, and 4/3 respectively. A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying ...
Philosophy of Arithmetic: Psychological and Logical Investigations (German: Philosophie der Arithmetik. Psychologische und logische Untersuchungen) is an 1891 book about the philosophy of mathematics by the philosopher Edmund Husserl. Husserl's first published book, it is a synthesis of his studies in mathematics, under Karl Weierstrass, with ...
In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early 1920s, [1] was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all ...