Talk:Möbius function: Difference between revisions
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:Zero is not a positive integer. The Möbius function is undefined at zero. No need to special case it. I don't see any examples that show a Möbius number for zero. Which ones are showing a value at zero? The only example that shows ANYTHING for an input of zero is the REXX example, and while that's a little odd, I wouldn't count it as wrong, as it specifically states that "bullet (•) to signify that a "null" is being shown (for the 0th entry)" ¯\_(ツ)_/¯ If REXX can't easily skip over zero, I'm not going to hold that against it. --[[User:Thundergnat|Thundergnat]] ([[User talk:Thundergnat|talk]]) 22:51, 25 January 2020 (UTC) |
:Zero is not a positive integer. The Möbius function is undefined at zero. No need to special case it. I don't see any examples that show a Möbius number for zero. Which ones are showing a value at zero? The only example that shows ANYTHING for an input of zero is the REXX example, and while that's a little odd, I wouldn't count it as wrong, as it specifically states that "bullet (•) to signify that a "null" is being shown (for the 0th entry)" ¯\_(ツ)_/¯ If REXX can't easily skip over zero, I'm not going to hold that against it. --[[User:Thundergnat|Thundergnat]] ([[User talk:Thundergnat|talk]]) 22:51, 25 January 2020 (UTC) |
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:: Sorry, my mistake that I thought I saw a zero being used for the input in showing the output (in fact, most programs inserted a blank (which I thought was a null being used for zero) to make the grid align with the others. Most of the programming solutions show a blank for the zeroth term, but that may just be an editing solution in showing a grid in leaving the place where a zero could/would be computed. Not knowing much about some languages, I misinterpreted what I observed. I've kept the REXX program to start at zero so as to make it look like (aligned with) all the other grids. I could special case the problem to ensure a blank is shown to align/match all the other grids, but I had already generalized the showing of a grid (even size 1). Sorry for all my confusion. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 23:34, 25 January 2020 (UTC) |
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:: If the REXX solution would show 199 entries, starting at unity, it would show something like (and make comparisons to other grids rather hard to visualize easily): |
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<pre> |
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1 -1 -1 0 -1 1 -1 0 0 1 -1 0 -1 1 1 0 -1 0 -1 0 |
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1 1 -1 0 0 1 0 0 -1 -1 -1 0 1 1 1 0 -1 1 1 0 |
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-1 -1 -1 0 0 1 -1 0 0 0 1 0 -1 0 1 0 1 1 -1 0 |
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-1 1 0 0 1 -1 -1 0 1 -1 -1 0 -1 1 0 0 1 -1 -1 0 |
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0 1 -1 0 1 1 1 0 -1 0 1 0 1 1 1 0 -1 0 0 0 |
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-1 -1 -1 0 -1 1 -1 0 -1 -1 1 0 -1 -1 1 0 0 1 1 0 |
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0 1 1 0 0 0 -1 0 1 -1 -1 0 1 1 0 0 -1 -1 -1 0 |
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1 1 1 0 1 1 0 0 -1 0 -1 0 0 -1 1 0 -1 1 1 0 |
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1 0 -1 0 -1 1 -1 0 0 -1 0 0 -1 -1 0 0 1 1 -1 0 |
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-1 -1 1 0 1 -1 1 0 0 -1 -1 0 -1 1 -1 0 -1 0 -1 |
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</pre> |
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Revision as of 23:36, 25 January 2020
Möbius function for positive integers
This task says to write a function to ... find the Möbius number for a positive integer n.
But it is also apparently being used to find the Möbius number for zero, a non-positive number, as zero is apparently the 1st term as shown in the task's first written example's output.
Could/should it be stated: ... find the Möbius number for a non-negative integer n ?
Or, should solutions treat zero as a special case? -- Gerard Schildberger (talk) 22:12, 25 January 2020 (UTC)
- Zero is not a positive integer. The Möbius function is undefined at zero. No need to special case it. I don't see any examples that show a Möbius number for zero. Which ones are showing a value at zero? The only example that shows ANYTHING for an input of zero is the REXX example, and while that's a little odd, I wouldn't count it as wrong, as it specifically states that "bullet (•) to signify that a "null" is being shown (for the 0th entry)" ¯\_(ツ)_/¯ If REXX can't easily skip over zero, I'm not going to hold that against it. --Thundergnat (talk) 22:51, 25 January 2020 (UTC)
- Sorry, my mistake that I thought I saw a zero being used for the input in showing the output (in fact, most programs inserted a blank (which I thought was a null being used for zero) to make the grid align with the others. Most of the programming solutions show a blank for the zeroth term, but that may just be an editing solution in showing a grid in leaving the place where a zero could/would be computed. Not knowing much about some languages, I misinterpreted what I observed. I've kept the REXX program to start at zero so as to make it look like (aligned with) all the other grids. I could special case the problem to ensure a blank is shown to align/match all the other grids, but I had already generalized the showing of a grid (even size 1). Sorry for all my confusion. -- Gerard Schildberger (talk) 23:34, 25 January 2020 (UTC)
- If the REXX solution would show 199 entries, starting at unity, it would show something like (and make comparisons to other grids rather hard to visualize easily):
1 -1 -1 0 -1 1 -1 0 0 1 -1 0 -1 1 1 0 -1 0 -1 0 1 1 -1 0 0 1 0 0 -1 -1 -1 0 1 1 1 0 -1 1 1 0 -1 -1 -1 0 0 1 -1 0 0 0 1 0 -1 0 1 0 1 1 -1 0 -1 1 0 0 1 -1 -1 0 1 -1 -1 0 -1 1 0 0 1 -1 -1 0 0 1 -1 0 1 1 1 0 -1 0 1 0 1 1 1 0 -1 0 0 0 -1 -1 -1 0 -1 1 -1 0 -1 -1 1 0 -1 -1 1 0 0 1 1 0 0 1 1 0 0 0 -1 0 1 -1 -1 0 1 1 0 0 -1 -1 -1 0 1 1 1 0 1 1 0 0 -1 0 -1 0 0 -1 1 0 -1 1 1 0 1 0 -1 0 -1 1 -1 0 0 -1 0 0 -1 -1 0 0 1 1 -1 0 -1 -1 1 0 1 -1 1 0 0 -1 -1 0 -1 1 -1 0 -1 0 -1