/sci/ - Science & Math

[Anonymous No.15944189]

>Smartpeepo intuitively understand maths without studying
BULL FUCKING HORSE SHIT

[Anonymous No.15944198]

>>15944189
Yeah I don't like how they're indexing either, but it does make sense since S is an arbitrary set of sins, so it's indexing by being arbitrary in it's implied super set. Terse but sensible.
Interesting if we take the limit of n we get 1/e

[Anonymous No.15944203]

>>15944189
Math is expressed like shit. On the other hand: Language is translated like shit too.
I think the "key" to looking at math is remembering two things:
1. Math is about counting. There will be some way of reformulating the question as "How many ... ?"
2. Math proofs, mathematical objects etc. /do something/, or at least /say something/. They're like parts of a machine, themselves made of parts. If you can see what the /aim/ is, you can work out what the /parts/ are doing. If you can work out what the parts are doing, you can see how their parts cause them to do what they do.
Like, with a proof, the most important thing to do to parse it is to work out what the "gist" is: What it's trying to do and how it's doing it.
Once you have that, you can then go down into the parts and figure out how they click into each other.
And it might be that looking at the parts causes you to revise what you think the overall goal actually was, which then itself causes another way of looking at the whole, which causes another way of looking at the parts.
At some point, the parts and the whole appear to line up. (Or don't, if the proof or the method is shitty.)

I'll see if I can work out what's going on in the pic.

[Anonymous No.15944221]

It would be easier to work out what's going on if you gave us a link to, or the name of, the text you're trying to comprehend.

[Anonymous No.15944227]

>>15944221
Page 560 of this

[Anonymous No.15944228]

>>15944227
>page 560
have you studied the preceding 559 pages?

[Anonymous No.15944232]

>>15944227
I'll whip it out, try to find it, and maybe post a YouTube video attempting to explain it if I can comprehend it.
My intuitive gist so far is that PIE is a way to count. It's a function that gives 0, -1 and 1 as outputs, depending on whether the input natural number is a multiple of a square (multiple of 4, 9, 25 etc.), or, if not, whether the input natural number is constructed by multiplying an even or odd number of prime numbers together.
This may be related to the shit involving i, since i is related to -1 and 1.
I think the idea is that we use this counting method (and perhaps later an inverse function of it), to determine other features of sets, or of sets of sets.
In this case, they're looking for (or have made) a function that tells you the number of people with 0 sins.
So this counting function appears to be involved, particularly given the (-1) to the power of something structure that resembles the formula of PIE.
I think using the word "sin" was some sort of attempt at humour given its similarity to the geometry word "sin", but that the two are probably not related.
Idk about the permutations, but perhaps there's a theme of counting. I'll have a look.

[Anonymous No.15944239]

>>15944189

Yes. People of x nature implicitly understand x. Both the nature and the understanding are absolutely predestined.

[Anonymous No.15944251]

>>15944239
That's too bad, because it limits information. Not that it really matters, considering. However, it would probably help teaching younger people if it was more accessible. However, that's not realistic, not with human language anyways. You'd need a new way to say things

[Anonymous No.15944264]

>>15944227
Are you reading this edition?: https://sites.math.rutgers.edu/~zeilberg/akherim/PCM.pdf

[Anonymous No.15944266]

>>15944228
>>15944239
>Smartpeepo implicitly understand maths
>Also you need to read the other 559 pages of a book to understand thid
Pick one you dishonest shits

[Anonymous No.15944274]

>>15944266
>>Smartpeepo implicitly understand maths
you can't even properly quote what OP actually wrote lol maths is the least if your problems dude you are probably a middle schooler

[Anonymous No.15944276]

I understand it fine. This author could explain more. Try reading the wikipedia page.

[Anonymous No.15944289]

>>15944227
Having gotten to it, being the poster whose post ended 232, I think it would be more wise for me to read the whole book.

[Anonymous No.15944419]

>>15944189
50 Math Tricks That Will Change Your Life Tanya Zakowich

[Anonymous No.15944424]

>enumerating sins

[Anonymous No.15944563]

>>15944189
Consider functions from the set of people to the set of integers. We can add, subtract, and multiply such functions to make new functions, and these addition, subtraction, and multiplication operations will respect the familiar laws of commutative rings with identity (addition and multiplication are commutative, associative, and have an identity; additive inverses exist; multiplication distributes over addition).

Given a set of people B, we can construct the indicator function [math]1_B[/math] which evaluates to 0 for people not in the set and evaluates to 1 for people in the set. The indicator function for the complement of B is [math]1 - 1_B[/math] (where 1 is the function that always evaluates to 1, which is the multiplicative identity). The indicator function for the intersection of B and C is the product of their indicator functions [math]1_B \cdot 1_C[/math]. And if we want to know the number of people in a particular set, we can sum its indicator function over all people.

We want to know the number of people who have no sins. The indicator function for the set of people with no sins is
[math]\left(1 - 1_{A_{\{s_1\}}}\right) \cdot \left(1 - 1_{A_{\{s_2\}}}\right) \cdots \left(1 - 1_{A_{\{s_n\}}}\right)[/math].
Distributing this out gives us
[math]\displaystyle \sum_S (-1)^{|S|} 1_{A_S}[/math]
where S ranges over all sets of sins. Then summing over all people gives us the expression in OP pic.

[Anonymous No.15944652]

>>15944189
I agree with >>15944198 that they should have explained what S is ranging over. It's possible to figure it out, but that's mostly on them.

Another technique that you can use to help understand what's going on is to look at small cases, such as n=2. In this case the formula says that the number of people without sins is
[math]|A_{\{\}}| - |A_{\{s_1\}}| - |A_{\{s_2\}}| + |A_{\{s_1,s_2\}}|[/math].

[math]A_{\{\}}[/math] is just the set of all people. Let's call this [math]X[/math]. A naive way to calculate the number of people with no sins would be
[math]|X| - |A_{\{s_1\}}| - |A_{\{s_2\}}|[/math]
but this would subtract people with both sins twice, leading to an inaccurate count. So the correct result is
[math]|X| - |A_{\{s_1\}}| - |A_{\{s_2\}}| + |A_{\{s_1,s_2\}}|[/math]
as the formula states.

[Anonymous No.15944663]

>>15944189
>weird E symbol
Just noticed this in OP. That symbol is the Greek letter sigma, and it's used in mathematics to represent sums. Look up "summation notation" or "sigma notation." Maybe review your high school textbooks or watch some Khan Academy videos.
https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/v/sigma-notation-sum

>"permutations" r/iamverysmart
That's not an attempt to sound smart, that's the usual word for that concept. The permutations of {1,2,3} are (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1).

>the ith sin is having [math]\pi[i] = i[/math]
Here [math]\pi[i][/math] means the ith number in the permutation [math]\pi[/math]. For example, if [math]\pi = (3,2,1)[/math], then [math]\pi[/math] has committed the 2nd sin, since the 2nd number in [math]\pi[/math] is 2.
(Obviously [math]\pi[/math] here is not being used to mean 3.14...)

[Anonymous No.15944689]

When I wrote >>15944563 I assumed a bit of familiarity with the basics of abstract algebra, but it can be simplified to not depend on that, possibly becoming clearer due to the extra explicitness required.

Given a set of people B, we can construct the indicator function [math]1_B[/math] which evaluates to 0 for people not in the set and evaluates to 1 for people in the set. That is,
[math]1_B(x) = 1[/math] when [math]x \in B[/math] and
[math]1_B(x) = 0[/math] when [math]x \notin B[/math].

The indicator function for the complement of B is
[math]1_{X \setminus B}(x) = 1 - 1_B(x)[/math].
(Capital X represents the set of all people.)

The indicator function for the intersection of B and C is
[math]1_{B \cap C}(x) = 1_B(x) \cdot 1_C(x)[/math].

The number of people in a set is the sum of the indicator function over the set of all people:
[math]\displaystyle |B| = \sum_{x \in X} 1_B(x)[/math]

The indicator function for the set of people with no sins is
[math]1_{(X \setminus A_{\{s_1\}}) \cap (X \setminus A_{\{s_2\}}) \cap \cdots \cap (X \setminus A_{\{s_n\}})}(x)[/math]
[math]= \left(1 - 1_{A_{\{s_1\}}}(x) \right) \cdot \left(1 - 1_{A_{\{s_2\}}}(x) \right) \cdots \left(1 - 1_{A_{\{s_n\}}}(x) \right)[/math].
Distributing this out gives us
[math]\displaystyle \sum_S (-1)^{|S|} 1_{A_S}(x)[/math]
where S ranges over all sets of sins.
(If this last step still mystifies you, try working it out yourself for n=2.)
Then summing over all people gives us the formula in OP for the number of people without sins.

[Anonymous No.15944706]

>>15944266
>Pick one you dishonest shits
are you retarded?
how do you expect to understand when you haven't even read the book you faggot?

[Anonymous No.15944717]

>>15944189
I agree it is bullshit. I am not super smart or anything but when I study hard for weeks or months I feel smarter. I take notes and ask questions and clarifications which I later read when I am back in my "dumb mode" and I am like wow was that really me? I don't even understand my own questions and thoughts. It is all about practice. It works exactly like working out. You can't be naturally ripped unless you lift all the same. Same thing with your brain. Nobody is naturally smart. Send a mathematician to a deserted island with no books or internet and provide coke and hookers then talk to him six months later. He will sound as dumb as you.

[Anonymous No.15944740]

Math is a language that is pretty much it. Only reason it seems so important is because british people are obsesses with pure language for no fuckin reason.

[Anonymous No.15944837]

>>15944189
it's just counting while excluding doubles in including triples again, etc.
suppose you want to know how many there are in these circles, then you count every red (including orange and purple), count every blue (likewise counting blue and purple) and green (likewise). but then you have counted green, purple and orange twice so you remove them ( (-1)^|S| ). but then you have removed brown once too much, so you count it again.

[Anonymous No.15944940]

>>15944717
Frfr nigga it do be like dat

[Anonymous No.15945671]

>>15944940
This is why I measure my value on my acts each day, everything that follows is my reward not my goal. My goal is just my direction, the act of moving it itself.

[Anonymous No.15945959]

>>15944740
It's a language where the vocabulary is massively doubled up on and means massively different things depending on context.

[Anonymous No.15946229]

>>15944189
They understand math, not retarded set theory proves of gods. It's literally misunderstanding shit what is like for 13 year old kids to know from school in western world.