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Examples include: "The sequence 1, 2, 3, ... continues ad infinitum." "The perimeter of a fractal may be iteratively drawn ad infinitum." The 17th-century writer Jonathan Swift incorporated the idea of self-similarity in the following lines from his satirical poem On Poetry: a Rhapsody (1733):
An argument which does not seem to have such a beginning becomes difficult to imagine. If it can be established, separately, that the chain must have a start, then a reductio ad infinitum is a valid refutation technique. reformatio in peius: change to worse: A decision from a court of appeal is amended to a worse one.
a mari usque ad mare: from sea to sea: From Psalm 72:8, "Et dominabitur a mari usque ad mare, et a flumine usque ad terminos terrae" (KJV: "He shall have dominion also from sea to sea, and from the river unto the ends of the earth"). National motto of Canada. amat victoria curam: victory favours care: Motto of several schools amicus certus in ...
The rhyme appears in De Morgan's A Budget of Paradoxes (1872) along with a discussion of the possibilities that all particles may be made of clustered smaller particles, "and so down, for ever", and that planets and stars may be particles of some larger universe, "and so up, for ever".
The following is a sample of books for further reading, selected for a combination of content, ease of access via the internet, and to provide an indication of published sources that interested readers may review. The titles of some books are self-explanatory.
Zeno's arguments may then be early examples of a method of proof called reductio ad absurdum, also known as proof by contradiction. Thus Plato has Zeno say the purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one."
On 5 April 2021, the "Logic" article first two paragraphs looked like this: Logic (from Greek : λογική, logikḗ , 'possessed of reason , intellectual , dialectical , argumentative ') is the systematic study of valid rules of inference , i.e. the relations that lead to the acceptance of one proposition (the conclusion ) on the basis of a ...
In the sci-fi spoof film Spaceballs, Director Mel Brooks includes a scene wherein the evil characters are viewing a VHS copy of their own story, which shows them watching themselves "watching themselves", ad infinitum. Perhaps the earliest example is in Homer's Iliad, where Helen of Troy laments: "for generations still unborn/we will live in ...