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All Mathematicians Please come to this thread

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B1rd

Endaris wrote:

4.0-5.0 with a margin of tolerance of like 0.25. For some psychological reason people will always pick closer to the higher number because they don't want to look like having small balls or something, i don't know. That's why it effectively plays out like 4.1-5.5*.
I don't know. Just use decimals.

You don't make sense, Khelly, it would be 3.01 to 5.99 if anything.
There can be no margin of tolerance. Even if you allow 0.1 star more it just becomes a slippery slope.
Deva

[Taiga] wrote:

4.00-5.00
Oh god finally some fucking common sense

OT:

HK_ wrote:

it means 4.00000000000000000000000000000000...1-4.99999999999999999999999999999999999...*
Saphirshroom

Khelly wrote:

Endaris wrote:

4.0-5.0 with a margin of tolerance of like 0.25. For some psychological reason people will always pick closer to the higher number because they don't want to look like having small balls or something, i don't know. That's why it effectively plays out like 4.1-5.5*.
I don't know. Just use decimals.

You don't make sense, Khelly, it would be 3.01 to 5.99 if anything.
Why would 4* mean 3.01 and not 4.00+? That doesn't make sense. Any map 3.99 or below does NOT have 4 stars.
This
Endaris

B1rd wrote:

There can be no margin of tolerance. Even if you allow 0.1 star more it just becomes a slippery slope.
Oh, so this is a full meme thread.
Reason:
Because 4-5= -1
This implies that the range of stars is |-1|=1
The only set of 1 that has both 4 and 5 in it is [4;5]

@Khelly: So you are some fucking compiler that is too stupid to round numbers when converting to integer. gg
Yuudachi-kun

Endaris wrote:

@Khelly: So you are some fucking compiler that is too stupid to round numbers when converting to integer. gg
I don't even get what you're trying to say.
Deva
lol rip
N0thingSpecial
I don't think maths even play a role in this topic lol since we're not using proper mathematical annotations in the first place
Yuudachi-kun

N0thingSpecial wrote:

I don't think maths even play a role in this topic lol since we're not using proper mathematical annotations in the first place
Here I can do non-notation too

4* maps --> All maps that have at least 4 stars and no more than 4.99
5* maps --> All maps that have at least 5 stars and no more than 5.99

4*-5* maps -> 4.00 to 5.99

"4-5" stars as a multi title

Ambiguous since the person reading might assume 4.00 to 5.00 or all 4 star and all 5 star maps.

Solution:

USE BETTER MULTI LOBBY TITLES YOU FUCKS
DeathHydra
Suddenly this topic is popular. I guess everyone is a mathematician
Saphirshroom

Endaris wrote:

@Khelly: So you are some fucking compiler that is too stupid to round numbers when converting to integer. gg
Every single compiler of every relevant programming language ever truncates when casting floating point to integers and doesn't round. (Also, this is the exact reason why I too think that 4-5* means 4.0 to 5.99.)
Khelly is right.
Endaris
Or they use the definition by the difficulty-grouping and think it is 3.5-5.5
N0thingSpecial
Wait let me ask a friend who is actually studying maths as a degree
Yuudachi-kun

Endaris wrote:

Or they use the definition by the difficulty-grouping and think it is 3.5-5.5

I never liked that rounding system to begin with. As an example, can you agree that I have a 7 star fc because of my #1 play because it's 6.8*? I don't.
-Makishima S-
4*-5* maps -> 4.00 to 4.99
You don't exclude last number in stack. Same as you cannot exclude first number from it.

[4* - 5*] = {4.00, 4.01, 4.02, ... , 4.98, 4.99, 5.00}
Yuudachi-kun

[Taiga] wrote:

4*-5* maps -> 4.00 to 4.99
You don't exclude last number in stack. Same as you cannot exclude first number from it.

[4* - 5* ] = {4.00, 4.01, 4.02, ... , 4.98, 4.99, 5.00}
I mistyped there 5.99 as 4.99 then I changed it to 5.00 because you confused me.
Sayorie


Are we done?
KanoSet

B1rd wrote:

There is a very complicated mathematical and philosophical problem that needs to be solved.
xd
from a philosophical view it's 3.5 - 5.5 because that what 4* and 5* taps have
Endaris

Arthraxium wrote:



Are we done?
Consider calculating the arithmetic mean of 4 and 5 as the sup and inf of our set
Then take the integral from 4 to 5 over the sinus of our arithmetic mean multiplied with pi.
DeathHydra

Arthraxium wrote:



Are we done?
Wow.

The image means 4.00-5.99 if anybody doesn't know
Deva
[iimx->4+f(x), limx->5-f(x)] :/
Dont laugh, at least i tried
Sayorie
To clarify, "4*-5*" can be really misleading, because there are two meanings which can be interpreted behind this:


Which means all the beatmaps between 4.0-5.0 star rating

or


Which means the set of all the 4-star beatmaps (beatmaps with 4 as the leading integer), plus all the 5-star beatmaps.

So the solution is to tell those MP basturds to clarify what they mean with the title.
DeathHydra
Or just make a room and don't rotate host. Therefore the title will always be right for you.
Sayorie
I don't multi, so I'm all gud.
Yuudachi-kun

Arthraxium wrote:

I don't multi, so I'm all gud.
Deva

Arthraxium wrote:

I don't multi, so I'm all gud.
Good idea. I will follow your example.
-Makishima S-
CE + dont buy supporter = perfect excuse to not go into multi
chainpullz

B1rd wrote:

There is a very complicated mathematical and philosophical problem that needs to be solved.

That is, does 4-5*, as in the context of the title for a multiplayer lobby mean 4.0-5.0*, or 4.0-5.99*, or something else entirely?

This needs to be solved once and for all. Let the debate begin.
4-5 typically translates to [4,5] \in \R unless you say "4-5 exclusive" in which case it translates to (4,5). So no, anything >5 would not be included.
TMiracle

Arthraxium wrote:


.
If only there was a way to put this equation in the lobby name.
Jellyfish McGub
it actually means 5-6

(but what is 5-6??)
GhostFrog

Arthraxium wrote:



Are we done?
We are most certainly not done. You haven't even defined f(x)! As near as I can tell, you intend for f(x) to be a many-valued function that takes on as values all maps with star ratings equal to the argument. From there, we have to define some sort of ordering on the set of maps in order to make sense of the interval. I guess the obvious choice is to consider all maps of the same star rating to be members of an equivalence class and then using the standard total order on real numbers over the star rating associated with each equivalence class.

However, I'm not entirely sure that this is what you meant because it raises some questions about your choice of notation. For one thing, I wonder why you would have chosen to use f(x) as boundaries of your interval, rather than choosing an interval for x and then indicating that we were accepting all f(x) for all x in that interval. It also makes me wonder why you used the limits, when you could, assuming I had correctly interpreted your notation, just as easily have chosen f(4) to be the lower limit and f(6) to be the upper limit. Your choice to use limits makes me think there must be some sort of discontinuity at x=4 and x=6 and it's not clear to me what would cause that to happen. Even more baffling is your choice to use one-sided limits. I honestly have no idea what quantity you could have had in mind that would have different limits from the left and the right that would make sense in the context in which you used them.

When we've sorted all of that out, we can get back to the very important argument taking place in this thread over trivial details.
Amianki
wtf
TakuMii
From what I've learned in Statistics class: If you have a range of 4 to 5, it will have boundaries that reach from 3.5 to 5.5. This would be a different story if the lobby were titled 4.0-5.0 (in which case the boundary would be 3.95-5.05), or even 4.00-5.00 (where the boundary is 3.995-5.005 and thus effectively ceases to matter unless you bother calculating the floating point values of each difficulty). Therefore, the game is mathematically correct in how it categorizes the difficulty ratings... people just need to start making better lobby titles.
Yuudachi-kun
Are you seriously trying to say people's usage of a star rating number should be measured with a confidence interval or something
TakuMii
No, I'm just saying that people should use more decimals.
Yuudachi-kun

YayMii wrote:

No, I'm just saying that people should use more decimals.
Yes.
GhostFrog
The convention YayMii is referring to comes from using significant figures. However, since star ratings are given to the nearest hundredth (and likely calculated to include significant figures beyond that), using significant figures to justify that convention is just silly. If someone means 3.5-5.5, they can simply say so. The relevant mathematical convention here would be that 4-5 means everything in the interval [4,5], where the square brackets indicate that the endpoints of the interval are included. Expecting people to all use that specific meaning is kind of ridiculous though.
Deva
Is any of this really relevant? I mean most of us dont play multi and if we do its with friends so why care?
If you dont play with friends shame on you
TakuMii
If we're speaking strictly mathematically, the star ratings are categorized by 1 significant digit, displayed to the hundredths (or 3 sigdigs for the majority of maps), and calculated at a floating point value. If only one digit is given in the lobby title, it should be mathematically safe to assume that anything within the class boundaries would be acceptable (given that this is how the game categorizes them anyways).
That being said, the limits of an actual lobby won't really have anything to do with mathematics, simply due to the fact that some people are more lenient than others when it comes to what they are willing to play although a lot people disapprove of my map choices regardless of difficulty lolrip.
GhostFrog

YayMii wrote:

If we're speaking strictly mathematically, the star ratings are categorized by 1 significant digit, displayed to the hundredths (or 3 sigdigs for the majority of maps), and calculated at a floating point value. If only one digit is given in the lobby title, it should be mathematically safe to assume that anything within the class boundaries would be acceptable (given that this is how the game categorizes them anyways).
That being said, the limits of an actual lobby have absolutely nothing to do with mathematics, simply due to the fact that some people are more lenient than others when it comes to what they are willing to play although a lot people disapprove of my map choices regardless of difficulty lolrip.
I think you're misunderstanding the point of significant figures.

Suppose you have a meter stick that's subdivided into centimeters. Further suppose that these centimeters are not subdivided into millimeters, but that markings have been made halfway between each consecutive pair of centimeter markings. If you use this meter stick and find that an object is between 33.5 and 34 cm long, you can round this result and say that the object is 34cm long. This measurement would have 2 significant figures. When performing calculations with this number, you would report the result of the calculations using a number of significant figures that's determined according to specific rules. These specific rules prevent rounding errors accumulated along the way from finding their way into the final answer.

I think it's safe to assume that the numbers used by the difficulty calculator have enough decimal places and enough significant figures that star ratings could be given to more than 2 decimal places without suffering from rounding errors accumulated along the way and they can certainly be given accurately to 2 decimal places. Including 3.5 when saying "4" isn't a matter of caring about significant figures, as this would be implying a degree of uncertainty that does not actually exist in the numbers used. The type of uncertainty that does exist in star ratings comes rather from algorithm imperfections, which very much do not respect mathematical rules of rounding or significant figures. A specific 5.6 star map may very well be easier for the average player than a specific 4.9 star map, for example, and a player may consider both of these to be de facto 5 star maps.

Some people do use "4-5" to mean "3.5 - 5.5", but in most cases, I would expect this to stem either from not wanting to use decimals (which makes the notation ambiguous) or from following the conventions the game uses when sorting maps by star rating. Using this convention on the basis of significant figures is simply not correct.
Kunino Sagiri
Even if they put a 3 star or a 6 star, I'll still play them so it's not like it matters too much. That's how multi worked when those "3.5-4.5*" "4-5*" "4-6*" memes were still not used.
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