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 Oct28 revised Polygonal tilings: differentiating between tiles and tilings, and their edges and vertices? added 724 characters in body Oct24 revised Polygonal tilings: differentiating between tiles and tilings, and their edges and vertices? I have rephrased my question, to hopefully clarify what I'm trying to ask. Oct23 asked Polygonal tilings: differentiating between tiles and tilings, and their edges and vertices? Jun21 asked $\sqrt{x + \sqrt{2x -1}} + \sqrt{x- \sqrt{2x-1}} = A$ Jan21 accepted Prime decomposition of an integer: methods of determining the prime factors $p_1, p_2, …, p_r$ and powers $k_1,k_2, …, k_r$ Jan21 revised Prime decomposition of an integer: methods of determining the prime factors $p_1, p_2, …, p_r$ and powers $k_1,k_2, …, k_r$ Edited title and content of question, adding query about prime factors Jan21 awarded Commentator Jan21 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. Jan21 asked Prime decomposition of an integer: methods of determining the prime factors $p_1, p_2, …, p_r$ and powers $k_1,k_2, …, k_r$ Jan19 accepted Representing Recursion and Primitive Recursion diagrammatically Jan19 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. Jan13 revised Representing Recursion and Primitive Recursion diagrammatically I've added logic and computability to the tags Jan13 revised Primitive recursive functions and characteristic functions. Methods of proof- examples. Illumination. edited tags; edited title Jan13 accepted Primitive recursive functions and characteristic functions. Methods of proof- examples. Illumination. Jan13 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'? Jan13 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(!) Jan13 revised Primitive recursive functions and characteristic functions. Methods of proof- examples. Illumination. added 2 characters in body Jan13 asked Primitive recursive functions and characteristic functions. Methods of proof- examples. Illumination. Jan12 awarded Teacher Jan12 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.