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Constructive proof. In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem), which proves the existence of a particular ...
Proof coinage refers to special early samples of a coin issue, historically made for checking the dies (as in demonstrating that something is true) and for archival purposes. In modern times, proofs are often struck in greater numbers, especially for coin collectors (numismatists). [1] Nearly all countries have issued proof coinage.
In contrast, a constructive proof establishes that a particular object exists by providing a method of finding it. The following famous example of a nonconstructive proof shows that there exist two irrational numbers a and b such that a b {\displaystyle a^{b}} is a rational number .
Collection. Numismatics portal. Money portal. v. t. e. This glossary of numismatics is a list of definitions of terms and concepts relevant to numismatics and coin collecting, as well as sub-fields and related disciplines, with concise explanations for the beginner or professional. Numismatics (ancient Greek: νομισματική, meaning ...
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not assume the law of the excluded middle and double negation ...
United States Proof Set. The United States Mint Proof Set, commonly known as the Proof Set in the United States, is a set of proof coins sold by the United States Mint. The proof set is popular with coin collectors as it is an affordable way to collect examples of United States coinage in proof condition.
e. In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as proofs of impossibility, negative proofs, or negative results. Impossibility theorems often resolve decades or centuries of work spent looking for a solution by proving there is no solution.
Proof theory is a major branch [1] of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed ...