Examples of using Theorems in English and their translations into Chinese
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Mathematics takes theorems as progress;
Writing those tests feels like proofing mathematical theorems.
Gödel's incompleteness theorems were an obstacle in one's attempt to talk about AI.
Elementary Fixed Point Theorems.
You need to be able to read theorems, and an ability to prove them will impress most people in the field.
Enter the No Free Lunch theorems.
The theorems are linked to each other in a directed manner by inference rules, forming a sort of dendritic network.
It stands in judgment over all philosophies, and its theorems are not ordinary proofs, but proofs about the provable.
In this paper, we consider a specific class of invariant and equivariant networks,for which we prove new universality theorems.
The Baire category theorem, needed to prove many important theorems, also requires a form of axiom of choice.
The incompleteness theorems are about formal provability within these systems, rather than about"provability" in an informal sense.
Wikipedia is also a very good resource and many formulas,theories and theorems are explained in a clear and comprehensible way.
Certainly the theorems which Galileo had proved on the centres of gravity of solids, and left in Rome, were discussed in this correspondence.
This fact contradicts the public image of mathematics,which is often seen as a closed world of theorems and arithmetic formulae.
For years physicists have used important theorems in linear algebra to quickly calculate solutions to the most complicated problems.
While getting into bed, I realised that I could apply to black holes the causalstructure theory I had developed for singularity theorems.
These might be the key theorems in math, the laws of thermodynamics in science or the relationship between supply and demand in economics.
In addition to traditional classroom discussions, computer technology and group exercises are used to allow students to explore geometric relationships anddiscover theorems.
This book takes some of the most important and paradigm-shifting theorems of mathematics and explains them in a clear and accessible fashion.
It is clear by these theorems that the sequent calculus does not change the notion of truth, because the same collection of propositions remain true.
The observation that many classically valid tautologies are not theorems of intuitionistic logic leads to the idea of weakening the proof theory of classical logic.
Fundamental theorems appear in ancient Egyptian work from 1820 BC, and later influences sprout from Babylonian, Ancient Greek, Chinese and Middle Eastern texts.
Logic is increasingly being used by computers-to prove mathematical theorems, to validate engineering designs, to encode and analyze laws and regulations and business rules.
And that Gödel's theorems do not lead to any valid argument that humans have mathematical reasoning capabilities beyond what a machine could ever duplicate.
Applications of mathematical theory, theorems, and methods to applied problems broaden the qualification to employment in a non-research environment.
Many very important theorems require the Hahn-Banach theorem, which relies on the axiom of choice that is strictly weaker than the Boolean prime ideal theorem.
Most of the classical identities are only theorems of intuitionistic logic in one direction, although some are theorems in both directions.
Many very important theorems require the Hahn-Banach theorem, usually proved using axiom of choice, although the strictly weaker Boolean prime ideal theorem suffices.