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**1 - 3**of**3**### Computability and analysis: the legacy of Alan Turing

, 2012

"... For most of its history, mathematics was algorithmic in nature. The geometric claims in Euclid’s Elements fall into two distinct categories: “problems, ” which assert that a construction can be carried out to meet a given specification, and “theorems, ” which assert that some property holds of a par ..."

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For most of its history, mathematics was algorithmic in nature. The geometric claims in Euclid’s Elements fall into two distinct categories: “problems, ” which assert that a construction can be carried out to meet a given specification, and “theorems, ” which assert that some property holds of a particular geometric

### Abstract On the Hierarchy of ∆ 0 2-Real Numbers

"... A real number x is called ∆0 2 if its binary expansion corresponds to a ∆02-set of natural numbers. Such reals are just the limits of computable sequences of rational numbers and hence also called computably approximable. Depending on how fast the sequences converge, ∆0 2-reals have different levels ..."

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A real number x is called ∆0 2 if its binary expansion corresponds to a ∆02-set of natural numbers. Such reals are just the limits of computable sequences of rational numbers and hence also called computably approximable. Depending on how fast the sequences converge, ∆0 2-reals have different levels of effectiveness. This leads to various hierarchies of ∆0 2 reals. In this paper we summarize several recent developments related to such kind of hierarchies. Key words: Computably approximable reals, ∆0 2-reals, hierarchy 1

### 6th Conference on Real Numbers and Computers

, 2004

"... Setting up the 6th conference on Real Numbers and Computers has been a great pleasure. Once again, we will bring together specialists from various research areas, all concerned with problems related to theoretical calculability or actual computations based on real numbers. These computations use man ..."

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Setting up the 6th conference on Real Numbers and Computers has been a great pleasure. Once again, we will bring together specialists from various research areas, all concerned with problems related to theoretical calculability or actual computations based on real numbers. These computations use many