Abstract: The paper is about formalization of Set Theory and Elementary Algebra theorems in mathematics and their proofs in a new programming language called LEAN 4 Theorem Prover. The paper describes ...

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Logic studies how arguments work, and how ideas can fit together. Decision theory studies how decisions should be made, especially under uncertainty. Game theory considers how we reason strategically, ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...

Get set theory explained in a clear and complete way, covering everything you need to know from basic definitions to key operations and ideas. This video walks through sets, subsets, unions, ...

We publish deeply researched (and often vastly underread) academic papers about our collective omnipresent media bias. We publish deeply researched (and often vastly underread) academic papers about ...

Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms. All of modern mathematics is built on ...

Teacher education often receives criticism for being too theoretical. Many students lack more training in how to teach in practice when they enter schools. They now receive this at the University of ...

The idea that we might be living inside a vast computer simulation, much like in The Matrix, has fascinated philosophers and scientists for years. But a new study from researchers at the University of ...

It's a plot device beloved by science fiction: our entire universe might be a simulation running on some advanced civilization's supercomputer. But new research from UBC Okanagan has mathematically ...