0_Wizard
7 is my favorite number, It is a natural number.
7 (seven; ) is the natural number following 6 and preceding 8.
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7
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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).
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.
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".
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.
Μ operator
In computability theory, the μ operator, minimization operator, or unbounded search operator searches for the least natural number with a given property. Adding the μ-operator to the five primitive recursive operators makes it possible to define all computable functions. Suppose that R( y, x, . ., x ) is a fixed "k+1"-ary relation on the natural numbers. The mu operator "μy", in either the unbounded or bounded form, is a "number theoretic function" defined from the natural numbers to the natural numbers. However, "μy" contains a "predicate" over the natural numbers that delivers "true" when the predicate is satisfied and "false" when it is not.
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.
Perfect digit-to-digit invariant
A perfect digit-to-digit invariant (PDDI) (also known as a Munchausen number) is a natural number that is equal to the sum of its digits each raised to the power of itself. A number "n" is a PDDI if and only if:  An example is 3435, as formula_2. The process of raising a number to the power of itself is known as tetration. The term "Munchausen number" was coined by Dutch mathematician and software engineer Daan van Berkel in 2009. Because each digit is raised by itself, this evokes the story of Baron Munchausen raising himself up by his own ponytail. Narcissistic numbers follow a similar rule, but in the case of the narcissistics the powers of the digits are fixed, being raised to the power of the number of digits in the number.