Search results
Results from the WOW.Com Content Network
An elementary proof is a proof which only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. For some time it was thought that certain theorems, like the prime number theorem, could only be proved using "higher" mathematics. However, over time, many of these ...
This is a list of axioms as that term is understood in mathematics. In epistemology , the word axiom is understood differently; see axiom and self-evidence . Individual axioms are almost always part of a larger axiomatic system .
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (axíōma), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.
Some math problems have been challenging us for centuries, ... The closest we’ve come—given some subtle technical assumptions—is 6. Time will tell if the last step from 6 to 2 is right ...
In mathematics, ideas are supposedly not accepted as fact until they have been rigorously proved. However, there have been some ideas that were fairly accepted in the past but which were subsequently shown to be false. The following list is meant to serve as a repository for compiling a list of such ideas.
In physics and mathematics, an ansatz (/ ˈ æ n s æ t s /; German: ⓘ, meaning: "initial placement of a tool at a work piece", plural ansatzes [1] or, from German, ansätze / ˈ æ n s ɛ t s ə /; German: [ˈʔanzɛtsə] ⓘ) is an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the solution by its results.
In applied fields the word "tight" is often used with the same meaning. [2] smooth Smoothness is a concept which mathematics has endowed with many meanings, from simple differentiability to infinite differentiability to analyticity, and still others which are more complicated. Each such usage attempts to invoke the physically intuitive notion ...
A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules. Discharge rules permit inference from a subderivation based on a temporary assumption. Below, the notation