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Design date. 2007. Presidential dollar coins (authorized by Pub. L. 109–145 (text) (PDF), 119 Stat. 2664, enacted December 22, 2005) are a series of United States dollar coins with engravings of relief portraits of U.S. presidents on the obverse and the Statue of Liberty ( Liberty Enlightening the World) on the reverse.
James Earle Fraser. Design date. 1913 (original), 2001 (modified) The American Buffalo silver dollar is a commemorative silver dollar issued by the United States Mint in 2001. [1] The coin commemorates both the National Museum of the American Indian and the Buffalo nickel, the latter serving as the basis for the dollar's design.
Design date. 2009–present. The Sacagawea dollar (also known as the " golden dollar ") is a United States dollar coin introduced in 2000, but subsequently minted only for niche circulation from 2002 onward. The coin generally failed to meet consumer and business demands. It is still generally accepted in circulation.
The quarter, formally known as the quarter dollar, is a denomination of currency in the United States valued at 25 cents, representing one-quarter of a dollar. Adorning its obverse is the profile of George Washington, while its reverse design has undergone frequent changes since 1998. Since its initial production in 1796, the quarter dollar has ...
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e. an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are ...
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
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