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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.
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 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.
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 ...
Cameo (coinage) Cameo finish. A standard uncirculated Lincoln cent. A Lincoln cent displaying deep cameo. In coin grading, cameo is the amount of contrast between the relief (raised or recessed design) and field (background). Cameo is usually seen on proof coinage, with the relief featuring a frosted finish and the field being mirror-like. [1]
Piedfort on the right. A piedfort [1] (UK: / p i ˈ eɪ f ɔːr t, ˈ p iː ɛ d ˌ f ɔːr t /, [2] [3] US: / p i ˌ eɪ ˈ f ɔːr, p i ˈ eɪ f ɔːr /; [4] [1] French: pied-fort or piéfort [5]) is an unusually thick coin, often exactly twice the normal weight and thickness of other coins of the same diameter and pattern.
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.
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 .