Theorems in the foundations of mathematics | Mathematical logic | Model theory | Nonstandard analysis | Universal algebra
The ultraproduct is a mathematical construction that appears mainly in abstract algebra and mathematical logic, in particular in model theory and set theory. An ultraproduct is a quotient of the direct product of a family of structures. All factors need to have the same signature. The ultrapower is the special case of this construction in which all factors are equal. For example, ultrapowers can be used to construct new fields from given ones. The hyperreal numbers, an ultrapower of the real numbers, are a special case of this. Some striking applications of ultraproducts include very elegant proofs of the compactness theorem and the completeness theorem, Keisler's ultrapower theorem, which gives an algebraic characterization of the semantic notion of elementary equivalence, and the RobinsonโZakon presentation of the use of superstructures and their monomorphisms to construct nonstandard models of analysis, leading to the growth of the area of nonstandard analysis, which was pioneered (as an application of the compactness theorem) by Abraham Robinson. (Wikipedia).
Don't do anything I did in this video. These capacitors are not designed to be shorted and doing so is dangerous. And no, you cannot make a welder out of these. I got hold of some 2600F capacitors that can dump hundreds of amps. Normally these are used in electric cars to handle sudden sto
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