Mathematical principles

mathematical lemma that, if 𝑛 items are put into 𝑚 containers, with 𝑛>𝑚, then at least one container must contain more than one item

counting technique in combinatorics

modern implementation of the method of indivisibles

theorem that a pointwise bounded set of linear operators on a Banach space is uniformly bounded in operator norm

combinatorial principle to determine possible ways to match disjoint sets.

counting principle in combinatorics

scientific principle

Statement that all sets of positive numbers contains a least element

concept in potential theory

mathematical statement

theorem that a holomorphic function’s absolute value cannot reach a strict local maximum at the interior of its domain

theorem

principle in Bayesian statistics

theorem that a harmonic function’s maximum can only be at the boundary of its domain

combinatorial principle that there exists a family of sets 𝐴(𝛼)⊆𝛼 for 𝛼<ω₁ such that for any 𝐴⊆ω₁, the set of 𝛼’s with 𝐴∩𝛼=𝐴(𝛼) is stationary in ω₁

combinatorial methods used in combinatorics, a branch of mathematics

principle that an integer equation can be solved by piecing together modular solutions

logical principle

principle of least length in physics

in constructive mathematics and computability theory, the axiom that given a decidable predicate on natural numbers, if it cannot be false for all numbers, then it is true for some number

Mathematical technique in complex analysis

mathematics principle in complex analysis

heuristics in measure theory