……解决停机问题。这是不可能完成的。事实证明柯西序列的表现更好，而且（稍微做点计算改进）你就能搞定很多事情。详情参见 Bishop 的书《Foundations of Constructive Analysis》。
…solving the halting problem. It cannot be done. It turns out Cauchy sequences are better behaved, and (with a bit computational improvement) you can make a lot of things work out. See Bihshop's book, Foundations of Constructive Analysis, for details.
……大约发展了40年左右，Beltrami 紧接着 Klein 才开始展示双曲几何为什么有趣且重要（据 Milnor[0]）。构造性数学到现在比那还要久远（《Foundations of Constructive Analysis》出版于1967年，而且哪怕在当时这个领域就已经不新了），那它在其他数学领域的应用在哪呢？我说的“应用”是指，比如平面的某些等距变换（PSL2(R)）……
…there is about 40-ish years into it Beltrami and then Klein started showing why hyperbolic geometry is interesting and important (per Milnor[0]). Constructive mathematics is older than that by now ('Foundations of Constructive Analysis' came out in 1967, and the field was old even then), where are its applications to other fields of math? By 'application' I'm meaning stuff like, for example, how certain isometries of the plane (PSL2(R))…
……解决停机问题。这是不可能完成的。事实证明柯西序列的表现更好，而且（稍微做点计算改进）你就能搞定很多事情。详情参见 Bishop 的书《Foundations of Constructive Analysis》。
…solving the halting problem. It cannot be done. It turns out Cauchy sequences are better behaved, and (with a bit computational improvement) you can make a lot of things work out. See Bihshop's book, Foundations of Constructive Analysis, for details.
……大约发展了40年左右，Beltrami 紧接着 Klein 才开始展示双曲几何为什么有趣且重要（据 Milnor[0]）。构造性数学到现在比那还要久远（《Foundations of Constructive Analysis》出版于1967年，而且哪怕在当时这个领域就已经不新了），那它在其他数学领域的应用在哪呢？我说的“应用”是指，比如平面的某些等距变换（PSL2(R)）……
…there is about 40-ish years into it Beltrami and then Klein started showing why hyperbolic geometry is interesting and important (per Milnor[0]). Constructive mathematics is older than that by now ('Foundations of Constructive Analysis' came out in 1967, and the field was old even then), where are its applications to other fields of math? By 'application' I'm meaning stuff like, for example, how certain isometries of the plane (PSL2(R))…