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Feb
6 |
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Can tests for the convergence and divergence of series be used to create undecidable sentences?
Very nice. I thought that something like this could be done but was not able to figure it out for myself. |
Feb
5 |
asked | Can tests for the convergence and divergence of series be used to create undecidable sentences? |
Jan
30 |
awarded | Popular Question |
Jan
24 |
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Two questions about the extent to which simple arcs and simple closed curves can fill up higher dimensional Euclidean spaces
I must apologize. I just discovered that my question (1) is a duplicate of MATHOVERFLOW.NET question No. 129867 which I asked nearly 3 years ago and which I had completely forgotten about. I received an affirmative answer at the time, but this time I am getting an added bonus-a demonstration of how to construct the arcs that have the property I was looking for. |
Jan
20 |
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Two questions about the extent to which simple arcs and simple closed curves can fill up higher dimensional Euclidean spaces
Many thanks for these very complete responses. I could never have found the proofs on my own. |
Jan
20 |
accepted | Two questions about the extent to which simple arcs and simple closed curves can fill up higher dimensional Euclidean spaces |
Jan
19 |
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Two questions about the extent to which simple arcs and simple closed curves can fill up higher dimensional Euclidean spaces
It could be the origin or any other point of E(n) which is fixed in advance. |
Jan
19 |
asked | Two questions about the extent to which simple arcs and simple closed curves can fill up higher dimensional Euclidean spaces |
Nov
14 |
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Comparing really big numbers
I can imagine the existence of a theory T which is an extension of Peano's Arithmetic (PA). Further T could be consistent if PA is. In T the relation "bigger than " could then be defined. There might be two numbers "a" and "b" which are both definable in T, whose definitions are such that each of the statements "a is bigger than b" and "b is bigger than a" are unprovable in T but are consistent with T when added as axioms to T. |
Nov
7 |
awarded | Nice Question |
Oct
14 |
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A question about simple closed plane polygons
Many thanks. That is a very nice way of getting a simple closed polygon through those n points. I wonder if it could be made to work in higher dimensional Euclidean spaces. I was also surprised ton learn that there is an actual formula for the maximum as a function of n. It looks like an asymptotic formula. Or is it just an upper bound. It is certainly an improvement on the crude upper bound n! |
Oct
14 |
accepted | A question about simple closed plane polygons |
Oct
13 |
asked | A question about simple closed plane polygons |
Oct
5 |
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A question about simple closed curves in 3-dimensional Euclidean space
I assume that C is the image of a continuous mapping whose domain is the closed unit interval. Thanks to both of you for very nice solutions of this problem. |
Oct
5 |
accepted | A question about simple closed curves in 3-dimensional Euclidean space |
Oct
4 |
asked | A question about simple closed curves in 3-dimensional Euclidean space |
Sep
22 |
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Can non-computable real numbers be defined without making use of any notions from computability theory
My statement of the modified Lebesgue covering problem is not quite correct. It should read "What is the minimum (or greatest lower bound) of the set of diameters of plane convex sets that cover every plane set having diameter 1" |
Sep
22 |
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Can non-computable real numbers be defined without making use of any notions from computability theory
Thanks for this reference. I will try to formulate some of these examples as geometric problems with specific real number solutions. |
Sep
21 |
asked | Can non-computable real numbers be defined without making use of any notions from computability theory |
Sep
7 |
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Is every computable real primitively recursively computable?
This is a very nice approach which looks as if it would work, although I do not know if I would be able to fill out all the details of a rigorous proof. It would seem, then, that we could define an ascending chain of subsets of the set of computable functions-starting with the set of primitive recursive functions- and classify a computable real number r by the smallest set in the chain containing a function that determines a Cauchy sequence of rational numbers which converges to r. |