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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 ...
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 ...
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 .
Proof coins. Like circulated grades, proof coins are graded on the Sheldon scale from 1 to 70, and are preceded by the abbreviation ‘PF’ or ‘PR’ to distinguish them from circulation strikes. Proof coins graded 60 to 70 are mirrored to those of Uncirculated grades with the difference that the coin was not made for circulation.
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 ...
The fundamental distinguishing characteristic of intuitionism is its interpretation of what it means for a mathematical statement to be true. In Brouwer's original intuitionism, the truth of a mathematical statement is a subjective claim: a mathematical statement corresponds to a mental construction, and a mathematician can assert the truth of a statement only by verifying the validity of that ...
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.
Both constructive and non-constructive proofs have been presented as "Cantor's proof." The popularity of presenting a non-constructive proof has led to a misconception that Cantor's arguments are non-constructive. Since the proof that Cantor published either constructs transcendental numbers or does not, an analysis of his article can determine ...