1. Computers have been used to prove mathematical theorems.

2. In proof theory, proofs and theorems are also mathematical objects.

3. This article focuses on prime ideal theorems from order theory.

4. Defined, an Axiomatic system is a set of axioms used to derive theorems

5. Analytica is an automatic theorem prover for theorems in elementary analysis

6. Related theory: definitions and rules, proof of algebraic formulas and theorems.

7. It was established above that the Ehrenfest theorems are consequences of the Schrödinger equation.

8. Mathematically, Corollary of theorems are used as the secondary proof for a complicated theorem

9. Finally, prime ideal theorems do also exist for other (not order-theoretical) abstract algebras.

10. Basic concepts, Conjectures, and theorems found in typical geometry texts are introduced, explained, and investigated

11. Probabilistic proof, like proof by construction, is one of many ways to show existence theorems.

12. Furthermore, we survey separation theorems for Biconvex functions which are mostly applied in probability theory.

13. Gives many equivalent statements for the BPI, including prime ideal theorems for other algebraic structures.

14. Fundamental Content of the similarity theory contains definition, theorems, type and methods of similitude.

15. Theorems of abstract algebra are powerful because they are general; they govern many systems.

16. He has established classic theorems concerning Cohen-Macaulay rings, invariant theory and homological algebra.

17. Generally, the technological or scientific advances in this area produce new theorems and algorithms.

18. He also proved several theorems concerning convergence of sequences of measurable and holomorphic functions.

19. Before the Disquisitiones was published, number theory consisted of a collection of isolated theorems and conjectures.

20. We prove charactarization theorems of a few algebraic structures with the help of their Annulets

21. This paper provides some theorems of the alternative for non-linear functions (sublinearconvex) between topological vector spaces.

22. They also used them to obtain proofs for fundamental theorems of each class of algebraic structures.

23. Kasparov’s Bivariant K-theory is used to prove two theorems concerning the Novikov higher signature conjecture

24. The formulation of such equations is based upon theorems regarding scalarvalued and tensor-valued tensor functions.

25. From a relatively short list of Axioms, deductive logic is used to prove other statements, called theorems or propositions

26. Continuity is an important concept in calculus because many important theorems of calculus require Continuity to be true

27. How do we prove triangles Congruent? Theorems and Postulates: ASA, SAS, SSS & Hypotenuse Leg Preparing for Proof

28. In addition, Kotschick proved further theorems about the structure of the space of the Chern numbers of smooth complex-projective manifolds.

29. The third approach, used in this video, is to use algebra and trigonometric limit theorems to evaluate limits Analytically…

30. Weak prime ideal theorems state that every non-trivial algebra of a certain class has at least one prime ideal.

31. Analytic geometry made great progress and succeeded in replacing theorems of classical geometry with computations via invariants of transformation groups.

32. 11 Many mathematicians simply set nettlesome questions like these aside and get back to the more pleasant business of proving theorems.

33. The paper gives several theorems for derivate of the function with finite limit at the infinite point and its strict proof.

34. This theorem and two additional fixed point theorems will be applied to linear and nonlinear algebraic equations and to nonlinear integral equations.

35. As with The Cattle Problem, The Method of Mechanical Theorems was written in the form of a letter to Eratosthenes in Alexandria.

36. Axiomatical consisting of a set of axioms from which theorems are derived by transformation rules Collins Discovery Encyclopedia, 1st edition © Explanation of axiomatic

37. Based on the above theorems, a new top-down algorithm for physical topology discovery is proposed, which can construct the whole topology utilizing the AFTs.

38. This result can be used to prove the completeness theorems of first order logic system and the universal refutation method proposed by us.

39. Hotz. Two new theorems on factorization of arbitrary transformations into embeddings and reductions and on product constructions involving non-lengthpreserving homomorphisms are derived.

40. He later changed his mind and submitted a thesis in 1926, titled Some theorems about integral solutions to certain algebraic equations and inequalities.

41. Those are only a few of the areas in which microeconomic theorems, methods and language have helped to achieve new and interesting results.

42. The ideal convexity of functionals is introduced and studied in this paper, four relation theorems between convexity and ideal convexity and an important counterexample are obtained.

43. As nouns the difference between Conjecture and theorem is that Conjecture is (formal) a statement or an idea which is unproven, but is thought to be true; a while theorem is (mathematics) a mathematical statement of some importance that has been proven to be true minor theorems are often called propositions'' theorems which are not very interesting in

44. Axiomatical consisting of a set of axioms from which theorems are derived by transformation rules Collins Discovery Encyclopedia, 1st edition © Explanation of Axiomatical

45. In Euclid's Elements, the first 28 propositions and Proposition I.31 avoid using the parallel postulate, and therefore are valid theorems in absolute geometry.

46. Each cardinal number is some Aleph (a consequence of the axiom of choice).However, many theorems about Alephs are demonstrated without recourse to the axiom of choice.

47. Axioma m (plural Axiomas) axiom (a truth based on an assumption) (mathematics) axiom (a fundamental assumption that serves as a basis for theorems) Related terms

48. However , the reader should realize that all properties of real numbers that are to be accepted as theorems must be deducible froom the axioms without any reference to geometry.

49. A specific aim of the RWHG project was to find a classification of algebraic structures that is defined by an analogue of the central limit theorems.

50. In this paper,[Sentencedict.com] the existence and uniqueness theorems of solution of a class Non-monotonic parametric stochastic operator equation with piecewise contraction property is discussed.

51. Comparing with the indexes of PR and PRE priority discipline queuing systems with service interruptions, we obtain some weak limit theorems for the workload and queuing length processes.

52. In this paper we demonstrate how the line integral, the surface integral, the theorems of Gauss and Stokes are taught with the help of a MAPLE computer algebra system (CAS).

53. The Baluga theorem requires a little more explanation (see the example below) than most poker theorems as it is a little more detailed, but it should be too hard to grasp

54. Establish that Fregean logics with theorems are all Assertional, and hence truth-equational, and that for a fully selfextensional logic, to be Assertional is the same as to be truth-equational

55. 18 It is able to change the law of excluded middle into all kinds of tautology through applications of the rule of equivalent replacement, and to prove all the inner theorems of propositional logic.

56. Hence, when taking the equivalent duals of all former statements, one ends up with a number of theorems that equally apply to Boolean algebras, but where every occurrence of ideal is replaced by filter.

57. Proof by Contradiction (also known as indirect proof or the technique or method of reductio ad absurdum) is just one of the few proof techniques that are used to prove mathematical propositions or theorems.

58. Many forms of these theorems are actually known to be equivalent, so that the assertion that "PIT" holds is usually taken as the assertion that the corresponding statement for Boolean algebras (BPI) is valid.

59. In logic, a rule of inference is Admissible in a formal system if the set of theorems of the system does not change when that rule is added to the existing rules of the system

60. The syllabus includes: Convex sets, functions, and optimization problems; basics of Convex analysis; least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems; optimality conditions, duality theory, theorems of alternative, and

61. Axiomatic Method means of constructing a scientific theory, in which this theory has as its basis certain points of departure (hypotheses)—axioms or postulates, from which all the remaining assertions of this discipline (theorems) must be

62. Besides sporadic occurrences of Adjunctions and Galois connections in important mathematical theorems, we discuss diverse contributions to a systematical theory of adjunction and residuation, and we touch on various applications to topology, logic, universal algebra and formal concept analysis.

63. In mathematics and logic, an Axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.A theory is a consistent, relatively-self-contained body of knowledge which usually contains an Axiomatic system and all its derived theorems

64. In mathematics and logic, an axiomatic system is any set of Axioms from which some or all Axioms can be used in conjunction to logically derive theorems.A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems

65. ‘The true antecedent of the modern vanishing point is Guidobaldo's punctum concursus (point of Concurrence).’ ‘The orthocenter is one of the four concurrency points in a triangle.’ ‘Theorems on Concurrence of lines, segments, or circles associated with triangles all deal with three or more objects passing through the same point.’

66. Bivariant K-theories generalize K-theory and its dual, often called K-homology, at the same time.They are a powerful tool for the computation of K-theoretic invariants, for the formulation and proof of index theorems, for classification results and in many other instances.The Bivariant K-theories are paralleled by different versions of cyclic theories which have similar formal

67. Theorems on Concurrence of lines, segments, or circles associated with triangles all deal with three or more objects passing through the same point.: Justice O'Connor made clear in her Concurrence, however, that the actual law's discrimination against homosexuals also provided a separate reason to strike it down.: The two events of selection and difference of race ought to be distinguished in