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Nov
11
comment What is it that determines the degree of a tile, and to what extent does the shape of a tile determine its degree?
I'm referring to any tiling of the plane initially- I suppose, an additional question would be, to what extent does the type of tiling affect my question? Presumably the degree of a tile, and the symmetry group must be interconnected?
Nov
11
comment What precisely is the difference between Euclidean Geometry, and non-Euclidean Geometry?
Thanks for an excellent illustration of how Euclidean and non-Euclidean Geometry differs, and you are very clear!
Jan
21
comment Prime decomposition of an integer: methods of determining the prime factors $ p_1, p_2, …, p_r$ and powers $k_1,k_2, …, k_r$
I haven't yet worked out the prime factors of this number. In fact, it could be divisible by any prime $\leq \sqrt{567788}$... So, actually, I'd be interested in learning methods of determining prime factors of large numbers too.
Jan
19
comment Representing Recursion and Primitive Recursion diagrammatically
Thanks for your excellent description of the difference between how primitive recursive and recursive functions behave. I can now see that the difference lies in the nature of the loops. Depicting this will be an interesting project- I'll have to post it on here, as and when I come up with something! Your book looks really interesting- I shall have to track it down.
Jan
13
comment Primitive recursive functions and characteristic functions. Methods of proof- examples. Illumination.
Thanks so much for your answer. I think I can see the thinking behind this now- well, I get how the algebra works anyway, and mostly get the rest of it... In answer to your questions- I am referring to f in the context of inferring the parity of n, i.e. $\chi_E$ This is what I meant by f and g doing the same thing. The overall topic in the textbook that I'm reading is 'characteristic functions'. Just one more thought- presumably $\chi_E$ would only be valid for the two cases 'n even' and 'n odd'?
Jan
13
comment Primitive recursive functions and characteristic functions. Methods of proof- examples. Illumination.
Ah, I did indeed miss out the 'n's! I see that f and g obviously don't do the same thing, but it is presumably no coincidence that g has been written in the way that it has. I think I'll sleep on that and take another look at it tomorrow(!)
Jan
12
comment Representing Recursion and Primitive Recursion diagrammatically
Thanks for your comment- it might well be the sort of thing I had in mind! Looks really interesting anyway. I have edited the second paragraph in my question, so that it is hopefully a little clearer what I mean. In general, I'm interested in any form of visual representation of recursion, and recursive functions.
Dec
30
comment Good introductory books on primitive recursive functions
Thanks for the excellent advice- I shall see if I can track those down!
Dec
30
comment Good introductory books on primitive recursive functions
Thanks for the tip!
Dec
30
comment Good introductory books on primitive recursive functions
Excellent- thanks!
Dec
30
comment Good introductory books on primitive recursive functions
Thanks so much for very useful suggestions!