| NOUN | proof by contradiction | - |
NOUN article.ind sg | pl
22 Übersetzungen
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Anwendungsbeispiele Englisch
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- Alhazen explored what is now known as the Euclidean parallel postulate, the fifth postulate in Euclid's "Elements", using a proof by contradiction, and in effect introducing the concept of motion into geometry.
- Proclus claimed to prove the infinite divisibility of a line, based on a proof by contradiction in which he considered the cases of even and odd numbers of points constituting it.
- The proof by contradiction shows that if it were possible to compute the Kolmogorov complexity, then it would also be possible to systematically generate paradoxes similar to this one, i.e.
- To prove that claim, we will proceed with a proof by contradiction. If there were a shorter path, then there can be two cases, either the shortest path contains another unvisited node or not.
- Zeno's arguments are perhaps the first examples of a method of proof called "reductio ad absurdum", also known as proof by contradiction.
- In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction.
- Hilbert produced an innovative proof by contradiction using mathematical induction; his method does not give an algorithm to produce the finitely many basis polynomials for a given ideal: it only shows that they must exist.
- In which case, if "P"1("S") is the set of one-element subsets of "S" and "f" is a proposed bijection from "P"1("S") to "P"("S"), one is able to use proof by contradiction to prove that |"P"1("S")| < |"P"("S")|.
- The following proof by contradiction uses a simple Pascal-like language to denote programs; for sake of proof simplicity assume its description (i.e. an interpreter) to have a length of [...] bits.
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