Pocklington's Theorem and Bertrand's Postulate

Pocklington's Theorem and Bertrand's Postulate The first four sections of this article include some auxiliary theorems related to number and finite sequence of numbers, in particular a primality test, the Pocklington's theorem (see [19]). The last section presents the formalization of Bertrand's postulate closely following the book [1], pp. 7-9.

[1]  Czeslaw Bylinski Some Basic Properties of Sets , 2004 .

[2]  Edmund Woronowicz Relations Defined on Sets , 1990 .

[3]  W. Neville Holmes,et al.  Binary Arithmetic , 2007, Computer.

[4]  Czeslaw Bylinski The Sum and Product of Finite Sequences of Real Numbers , 1990 .

[5]  Czeslaw Bylinski Functions from a Set to a Set , 2004 .

[6]  Andrzej Trybulec,et al.  On the Sets Inhabited by Numbers 1 , 2003 .

[7]  Y. Shidama,et al.  Lebesgue Integral of Simple Valued Function , 2007 .

[8]  Piotr Rudnicki,et al.  Multivariate Polynomials with Arbitrary Number of Variables 1 , 2004 .

[9]  G. Bancerek The Fundamental Properties of Natural Numbers , 1990 .

[10]  Czeslaw Bylinski Functions and Their Basic Properties , 2004 .

[11]  A. Kondracki Basic Properties of Rational Numbers , 1990 .

[12]  Wojciech A. Trybulec Non-contiguous Substrings and One-to-one Finite Sequences , 1990 .

[13]  Edmund Woronowicz Relations and Their Basic Properties , 2004 .

[14]  Czesław Bylí Finite Sequences and Tuples of Elements of a Non-empty Sets , 1990 .

[15]  Kenneth Halpern August The Cardinal Numbers , 1888, Nature.

[16]  Józef Białas Infimum and Supremum of the Set of Real Numbers. Measure Theory , 1990 .

[17]  ANDREW GRANVILLE THE FUNDAMENTAL THEOREM OF ARITHMETIC , 1998 .

[18]  Noboru Endou Definitions and Basic Properties of Measurable Functions , 2004 .

[19]  J. Harrison Formalized Mathematics , 1996 .

[20]  Krzysztof Hryniewiecki,et al.  Basic Properties of Real Numbers , 2004 .

[21]  M. Aigner,et al.  Proofs from "The Book" , 2001 .

[22]  Andrzej Trybulec,et al.  Binary Operations Applied to Functions , 1990 .

[23]  Yuji Sakai,et al.  Properties of Partial Functions from a Domain to the Set of Real Numbers , 1992 .

[24]  Józef Białas Some Properties of the Intervals , 2004 .

[25]  Y. Shidama,et al.  Lebesgue Integral of Simple Valued Function 1 , 2005 .

[26]  Beata Perkowska,et al.  Functional Sequence from a Domain to a Domain , 1992 .

[27]  G. Ivanov Definition of Convex Function and Jensen ’ s Inequality , 2004 .

[28]  Józef Bia las The σ-additive Measure Theory , 1990 .

[29]  A. Kondracki,et al.  The Chinese Remainder Theorem , 2019, Certain Number-Theoretic Episodes in Algebra.

[30]  Noboru Endou The Measurability of Extended Real Valued Functions , 2000 .

[31]  W. Kellaway,et al.  Complex Numbers , 2019, AMS/MAA Textbooks.

[32]  G. Bancerek,et al.  Ordinal Numbers , 2003 .

[33]  Grzegorz Bancerek,et al.  Joining of Decorated Trees , 2004 .

[34]  Andrzej Ne ' dzusiak Fields and Probability , 1990 .

[35]  Józef Bia Series of Positive Real Numbers . Measure Theory , 1990 .

[36]  Martin Aigner,et al.  Proofs from THE BOOK , 1998 .

[37]  Czeslaw Bylinski Binary Operations Applied to Finite Sequences , 1990 .

[38]  Colin R. Fletcher,et al.  The Fundamental Theorem of Arithmetic Dissected , 1997 .

[39]  Czeslaw Bylinski,et al.  Basic Functions and Operations on Functions , 1989 .

[40]  A. Trybulec Tarski Grothendieck Set Theory , 1990 .

[41]  Grzegorz Zwara,et al.  The Divisibility of Integers and Integer Relatively Primes 1 , 1990 .

[42]  Rafa l Kwiatek Factorial and Newton coeffitients , 1990 .