0_Wizard
Hi there! This is a funny question but what is your favorite number? Mine is 7 which is the natural number following 6 and right before 8
7 (seven; ) is the natural number following 6 and preceding 8.
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7
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Prime number
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 6 is composite because it is the product of two numbers () that are both smaller than 6. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.
Wieferich prime
In number theory, a Wieferich prime is a prime number "p" such that "p" divides , therefore connecting these primes with Fermat's little theorem, which states that every odd prime "p" divides . Wieferich primes were first described by Arthur Wieferich in 1909 in works pertaining to Fermat's last theorem, at which time both of Fermat's theorems were already well known to mathematicians. Since then, connections between Wieferich primes and various other topics in mathematics have been discovered, including other types of numbers and primes, such as Mersenne and Fermat numbers, specific types of pseudoprimes and some types of numbers generalized from the original definition of a Wieferich prime.
Natural number
In mathematics, the natural numbers are those used for counting (as in "there are "six" coins on the table") and ordering (as in "this is the "third" largest city in the country"). In common language, words used for counting are "cardinal numbers" and words used for ordering are "ordinal numbers". Some definitions, including the standard ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with 1, corresponding to the positive integers . Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers (including negative integers).
Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of whether number theory is consistent and complete. The need to formalize arithmetic was not well appreciated until the work of Hermann Grassmann, who showed in the 1860s that many facts in arithmetic could be derived from more basic facts about the successor operation and induction.
Mathematical induction
Mathematical induction is a mathematical proof technique, a form of direct proof, usually done in two steps. It is used to prove a given statement about any well-ordered set. Most commonly, the well-ordered set is the set of natural numbers. The first step, called the base case or basis, proves that the theorem is true for the number one. The second step, called the inductive step, proves that, if the theorem is true for a given number, then it is also true for the next number. These two steps establish the theorem for all natural numbers. The fact that these two steps prove that a theorem is true in an infinite number of cases is called the "Principle of mathematical induction".
0
0 (zero; ) is both a number and the numerical digit used to represent that number in numerals. The number 0 fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems. Names for the number 0 in English include zero, nought (UK), naught (US) (), nil, or—in contexts where at least one adjacent digit distinguishes it from the letter "O"—oh or o (). Informal or slang terms for zero include zilch and zip. "Ought" and "aught" (), as well as "cipher", have also been used historically.
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers.
1_Apprentice
Mine happens to be 7 as well! Many seems to associate 7 as being a lucky number.