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This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras. List of algorithms. List of axioms. List of conjectures. List of data structures. List of derivatives and integrals in alternative calculi. List of equations.
Then P(n) is true for all natural numbers n. For example, we can prove by induction that all positive integers of the form 2n − 1 are odd. Let P(n) represent " 2n − 1 is odd": (i) For n = 1, 2n − 1 = 2 (1) − 1 = 1, and 1 is odd, since it leaves a remainder of 1 when divided by 2. Thus P(1) is true.
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as ...
Cross-figure. A cross-figure (also variously called cross number puzzle or figure logic) is a puzzle similar to a crossword in structure, but with entries that consist of numbers rather than words, where individual digits are entered in the blank cells. Clues may be mathematical ("the seventh prime number"), use general knowledge ("date of the ...
The Pythagorean theorem has at least 370 known proofs. [1]In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. [a] [2] [3] The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.
Kakuro or Kakkuro or Kakoro (Japanese: カックロ) is a kind of logic puzzle that is often referred to as a mathematical transliteration of the crossword. Kakuro puzzles are regular features in many math-and-logic puzzle publications across the world. In 1966, [1] Canadian Jacob E. Funk, an employee of Dell Magazines, came up with the ...
The form of a modus ponens argument is a mixed hypothetical syllogism, with two premises and a conclusion: If P, then Q. P. Therefore, Q. The first premise is a conditional ("if–then") claim, namely that P implies Q. The second premise is an assertion that P, the antecedent of the conditional claim, is the case.
With Peirce's law, one can add (at no cost) additional premises of the form Z→P to Γ. For example, suppose we are given P→Z and (P→Q)→Z and we wish to deduce Z so that we can use the deduction theorem to conclude that (P→Z)→(((P→Q)→Z)→Z) is a theorem. Then we can add another premise Z→Q. From that and P→Z, we get P→Q.