Lesson plan
Universal function
A universal function is a function that can, in some defined way, imitate all other functions. This occurs in several contexts: * In computer science, a universal function is a computable function capable of calculating any other computable function. It is shown to exist by the UTM theorem. * In cryptography, a universal one-way function is a function that is known to be one-way if one-way functions exist. * In mathematics, a universal function is one that contains subregions that approximate every holomorphic function to arbitrary accuracy. The Riemann zeta function (and some others) have this property, as described in Zeta function universality.
Article summary
A universal function is a function that can, in some defined way, imitate all other functions. This occurs in several contexts: * In computer science, a universal function is a computable function capable of calculating any other computable function. It is shown to exist by the UTM theorem. * In cryptography, a universal one-way function is a function that is known to be one-way if one-way functions exist. * In mathematics, a universal function is one that contains subregions that approximate every holomorphic function to arbitrary accuracy. The Riemann zeta function (and some others) have this property, as described in Zeta function universality.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.