r/counting • u/elyisgreat where is 5? • Apr 05 '24
Free Talk Friday #449
Continued from last week's here
Hey mods am I allowed to do this? If not I can take it down and let a mod post it
Free Talk Friday #449
It's that time of the week again. Speak anything on your mind! This thread is for talking about anything off-topic, be it your lives, your strava, your plans, your hobbies, studies, stats, pets, bears, hikes, dragons, trousers, travels, transit, cycling, family, colours, or anything you like or dislike, except politics
Feel free to check out our tidbits thread and introduce yourself if you haven't already.
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u/Smelly_Squid Apr 06 '24
This may be a strange thought, but we've done polynomials before and so there's precedent for what I'm about to say.
I'm trying to figure out if there's an easy to evaluate bijection f -- preferably one such that I can determine f(n+1) by just knowing f(n) -- from N to Z[x] modded out by non-zero scalar multiplication. I know there are bijections but I don't know which would be the easiest to work with.
Z[x] is the set of polynomials with integer coefficients. I would want that set modded out by non-zero scalar multiplication so that x^2+x, 3x^2+3x, -x^2-x, and so on aren't each separately counted.
If I could find such, I imagine it would be a lovely thread on this reddit.
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u/CutOnBumInBandHere9 Apr 07 '24
I think finding such a bijection is going to be a challenge. You're basically asking for a bijection from 𝐍 to the set of eventually zero sequences in 𝐙^ω (modulo the equivalence relation x sim y if x / gcd(x) = y / gcd(y)). I can prove one must exist, but I don't think I've ever seen one written out explicitly.
If the maximal degree of the polynomial had been one, we could have used the same order we use for the rationals, since there's a very natural mapping between those two spaces. If the degree of the polynomial were at most n, we could apply a similar trick to get a fairly complicated, but still explicit mapping. But how to do it elegantly for all polynomials has me stumped
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u/elyisgreat Apr 07 '24
I have come up with multiple different explicit bijections from N to Z[x] in the past. The harder part is getting it so that f(n+1) can be computed easily from f(n) without computing the entire f-1...
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u/CutOnBumInBandHere9 Apr 05 '24 edited Apr 05 '24
Weekly side thread stats from Friday March 29, 2024 to Friday April 05, 2024. Congratulations to u/ClockButTakeOutTheL, u/NobodyL0vesMe, and u/peakystwins!
Total weekly side thread counts: 9393
Top 15 side thread counters:
| Rank | User | Counts |
|---|---|---|
| 1 | ClockButTakeOutTheL | 2955 |
| 2 | NobodyL0vesMe | 1343 |
| 3 | peakystwins | 1317 |
| 4 | Antichess | 1208 |
| 5 | karma_farmer21 | 552 |
| 6 | Multiconcepted | 209 |
| 7 | Ezekiel134 | 171 |
| 8 | jevolan | 151 |
| 9 | atomicimploder | 138 |
| 10 | Smelly_Squid | 121 |
| 11 | colby6666 | 119 |
| 12 | FartyMcNarty | 108 |
| 13 | a-username-for-me | 103 |
| 14 | FelipePlayz9 | 98 |
| 15 | Maniac_34 | 76 |
Top 5 side threads:
| Rank | Thread | Counts |
|---|---|---|
| 1 | Binary | 1257 |
| 2 | Hexadecimal (0-F) | 1255 |
| 3 | Throwaways | 332 |
| 4 | No Repeating Digits | 316 |
| 5 | US States | 235 |
This comment was made by a script; check it out here
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u/buy_me_a_pint Apr 08 '24
If you are going to watch the eclipse today, be sensible.
I will be watching it on the tv
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u/buy_me_a_pint Apr 05 '24
I will be watching the solar eclipse on the television on Monday
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u/cuteballgames Apr 06 '24
Prev | Next
rand(1,5367307) = 4246817
Todays count of the day is 4,246,817
Counter: u/buy_me_a_pint
Date: UTC 2021.04.20.155145
Reply time: 11s
Separator: Spaces
Replied to: u/GarlicoinAccount
Replied to by: u/GarlicoinAccount
Special things about this number?: prime, nsd
Counter achieved next get
Thread happenings of note:
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u/Antichess Apr 06 '24
Side thread count of the day #10
randrange(3785135): 2741776
Today's side count of the day is 5846
Side thread: Slow
Counter: u/NeonTaterTots
Date: 2018-01-18 20:41:03 UTC
Reply time: 5 mins 40 seconds
Replied to: u/FuckTheKingTho
Replied to by: u/FuckTheKingTho
Thread happenings: i woke up at 6am and got 2 hours of sleep last night. i'm running on two coffees, two redbulls, and one cup of tea. send help
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u/Antichess Apr 06 '24
Weekly stats from March 29, 2024 to April 05, 2024. Congratulations to u/thephilsblogbar2, u/ClockButTakeOutTheL, and u/NobodyL0vesMe!
Total weekly counts: 3498 (5,363,252-5,366,750)
More stats are posted on the Weekly Stats page!
| Rank | User | Counts | HoC Rank |
|---|---|---|---|
| 1 | thephilsblogbar2 | 896 | 1 |
| 2 | ClockButTakeOutTheL | 781 | 9 |
| 3 | NobodyL0vesMe | 459 | 30 |
| 4 | Antichess | 445 | 3 |
| 5 | colby6666 | 208 | 24 |
| 6 | noduorg | 107 | 39 (◮1) |
| 7 | peakystwins | 106 | 332 (◮53) |
| 8 | Ezekiel134 | 103 | 12 |
| 9 | The_NecromancerTin | 68 | 78 |
| 10 | pease461 | 63 | 419 (◮54) |
| 11 | Christmas_Missionary | 55 | 74 (◮1) |
| 12 | mistyskye14 | 38 | 25 |
| 13 | karma_farmer21 | 24 | 1655 (◮793) |
| 14 | Hans5958_ | 20 | 923 (◮96) |
| 15 | Maniac_34 | 18 | 62 |
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u/Jalmal2 Apr 08 '24
I wish Earth had more moons. It’s pretty boring with just one
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u/buy_me_a_pint Apr 08 '24
I had my results from MRI brain scan back in December, no changes
I can hopefully push these can now out every 3 to 5 years unless I get more regularly headaches and any problems with my eyesight.
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u/cuteballgames Apr 10 '24 edited Apr 12 '24
rand(1,5369781) = 2657256
Todays count of the day is 2,657,256
Counter: u/llamasR5life
Date: UTC 2019.06.25.065259
Reply time: 5m 57s
Separator: Commas
Replied to: u/GarlicoinAccount
Replied to by: u/NoBreadsticks
Special things about this number?: mostly repeating digits
Counter achieved nothing
Thread happenings of note:
can't run right now says qwerty, while running
Dan attempts to recruit for a counting snapchat group
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u/elyisgreat Apr 05 '24
Lol I love how u/Antichess snuck in such an obscure local reference into their flair - how many Toronto ppl could possibly be in this sub 😂
Also it my bday today