How come you divide by the permutations that are identical rather than subtracting?
I have been spending quite a bit of time thinking about this, though I have not come up with any formal reasons.
The closest thing my brain can put together is that you have some multiplicative rather than additive "overcounting".
Is it even possible to formally prove counting formulas like this without appealing to intuition?
Why is the product rule correct even?
>>7798300
Think about grouping the original [math] 5 ! [/math] permutations into groups of two, each one containing the two permutations of [math]P_1[/math] and [math]P_2[/math] within that particular permutation of HAPPY.
For instance, one of the groups might be { H P[math] _1[/math] Y P [math] _2 [/math] A , H P[math] _2[/math] Y P [math] _1 [/math] A }.
The two elements in each group are identical, and elements in different groups are not identical, so we care about the number of groups. If there are 120 elements and we put them in groups of 2, there are 120 / 2 groups.
You can generalize this visual understanding to the general case, and to formally prove counting formulas like this without appealing to intuition.
>Is it even possible to formally prove counting formulas like this without appealing to intuition?
It is more subtle than that.
Math is defined in such a way that these intuitive rules are correct. If you accept the fact that it is a reasonable model (which it is), then you might say that you have "proved" this intuitive thing.
But really, all you did is create a mathematical model of what you were talking about, prove things about your model, then interpret the result as a property of the initial object.
>Why is the product rule correct even?
If you have a bag containing objects coming in m shapes and n colours such that, for each shape, there is exactly one object of each colour, then you have mn objects.
Indeed, to count the objects, you may group them by shape: you then get m disjoing groups, each containing n objects. The total number of objects is the sum of the number of objects in each group, that is m times n.
You may formalize this argument using sets but that's basically the idea.
>>7798321
so with 3 identical elements, each group would have 3! elements one for each ordering that otherwise appears identical? Diving makes sense to me here I think, the grouping explanation helps.
How does the multiplication (or repeated division) of group numbers when there are several groups of repeat elements like AABBC work out?
>>7798351
Well putting it that way makes it sound pretty sensible.
Taking the SAT this weekend, what can I expect?
>>7798285
>what can I expect?
An underage ban
>>7798290
/thread
>>7798285
a joke
Going to school after a long hiatus. Taking Calculus in August and have never took preCal or Trig. Can anyone recommend some good books I can get on Amazon to learn everything I need to go into Calculus?
>>7798258
Didn't we have a wikia for this?
>>7798336
Post a throwaway email and i can send you all my tests hw and my precalc book in a neat zip file
Planet X.... .... ..... ....
... .. .. .. .. .. ....
... . .. . . . .. . .. . ..
.........is real!!@!
science says so.
> a new planet in our solar system
> not even in our solar system
This planet doesn't even orbit the sun. It orbits around some other bitch ass gravity source. Fuck this deceptive piece of shit rock.
>>7798071
Yes it does orbit the Sun.
>>7798055
Why do people care so much?
For me, it makes sense that people and popsci would be interested in mars. It is great and exciting when news come that there is water and all the shit that will make it one day possible for us to colonize it. It is interesting.
Then you people start talking about fucking frozen lumps of gas and I realize that popsci is food for retards.
Anyone here work in GMP biotech?
I need help being social
cyclic GMP?
>>7797875
>I need help being social
Stop being a pussy faggot then.
>>7797910
lol no babby some of us are career scientists
Was there literally any new concept art/spaceships/whatever in this movie?
> blow up le 3 planets with sun power xDD
> mazda bukkake shitty cgi character
> whole cantina scene as cringeworthy as jabbas palace in the new episode 6
>>7797839
also, forgot about Han Solos spaghetti monsters
Tell that to the >>>/tv/ club
Is non-existence unfathomable or is it just impossible?
>>7797809
shit those are cool figures, gotta cop me some perhaps. Not a photographer though but that would be so cool
also could you fuck off with these shitty threads, it seems like 14 year-olds on /b/ have some great idea they think is so new and worth pondering so they look for a philosophy board and don't find one, so they come to /sci/
fuck
off
>>7797809
Is shitposting unfathomable or is it just infinite?
>>7797817
Thanks for the reply friendo :)
Thought:
Suppose someone has refractory problems leading to far sightedness. They can read something if it is of a certain size and distance.
The question is, is it absolute distance from the letters, or is it relative distance?
For instance, would a person with short sightedness, who couldn't read something directly in front of them from 6 feet away be able to read it if they had a mirror reflecting the letters that are 6 feet away at a 45 degree angle next to them? It should mean that if it is a problem with focusing or light gathering, the information is coming from 1 foot away now instead of 6 feet.
Is it possible to use this as a test to determine whether eyesight problems are psychosomatically created?
Asking because of
http://www.scientificamerican.com/article/your-thoughts-can-release-abilities-beyond-normal-limits/
>They took a vision test while “flying” the simulator. A control group took the same vision test in the cockpit while the simulator was inactive. People’s vision improved only if they were in the working simulator.
>To rule out the possible effect of motivation, the researchers brought another group of people into the cockpit and asked them to read a brief essay on motivation. After people finished reading, they were strongly urged to be as motivated as possible and try hard to perform well in the vision test. The test was conducted while the simulator was inactive. They did not show a significant improvement.
>In an eye exam, we are used to start experiencing problems at the bottom third of the eye chart, where letters start to get small. In another experiment, Ellen Langer and colleagues showed people a shifted chart. At the top, it included letters equivalent to the medium-size letters on the normal eye chart and the chart progressed to letters of very small size at the bottom. Because people were expecting to read the top two thirds of the shifted chart as well, they were able to read much smaller letters.
>>7797388
Dam son. Guess all those people who make spectacles been wasting their time. Pretty cool.
>>7797454
just wondering
Groups of numbers that are equal
1 - 0
2 - 0
3 - 1 - 1,2;3
4 - 1 - 1,4;2,3
5 - 0
6 - 0
Ect
How do I math these
wat chu talkin bout fgt :v
>>7797301
Ha! There's still no proof of this even though the ancient Egyptians were already working at this. It's not a famous theorem, but at the same time very important and difficult to work out even with the most advanced of mathematicians. Postulates have been made on how to math these but there's no verification..... yet....
We need a modern bright mind like Gauss to shed light on this.
[citation needed]
if someone is inside a crate filled with water and falls from a height high enough to kill someone will they survive?
pic related
>>7797134
1. How large is the crate?
2. How large is the person?
3. How heavy is the crate?
4. Exactly how high up was the crate when it was dropped?
5. What material is the crate made out of?
6. Why the fuck do you need to know?
7. No.
>>7797140
i just wanna know if under any circumstances it will work from a deadly height like 100ft
>>7797134
It depends on many factors persons weight, volume, waters density and type, type of material, dimensions of crate to determine weight. Please be more specific.
What do you guys think of optical rotation, chirals, and especially knot theory? I really had just been memeing myself into thinking that i like science just because i declared my major and i have a while to go to actually take the science courses i need. but reading up on this stuff, and these particular things, its really interesting. the fact that very dilute solutions follow mathematical laws was really mind blowing to me. also the descriptions used within the definition of chiral and to a much broader concept, knot theory, i really am amazed why i haven't been using my time like this before
Bump i thought sci was supposed to be intelligent
>>7796795
First, your post is a fucking a blog.
>I chose my major. I got interested in science. The fact that we can explain thing with math (WOW!) blew my mind. lol my life is so important and I bet it is very interesting to you too!
Second, asking us what we think about something is not a science question.
Just like 'What do you guys think about physics?' Is not a physics question
So yeah, sci is supposed to be intelligent. And as I can see, you are supposed to be a dumbfuck so I think you better downgrade your expectations and post this again but in /b/ or any other place with people of your... mental abbility.
>>7796712
optical rotation is pretty cool. you can induce circular birefringence in atomic vapours by introducing an external magnetic field. dat zeeman effect bruh
If they made unbreakable combs why aren't we building space ships out of them?
>>7796526
because space isn't made of hair
>>7796531
dude
What exactly did he contribute, /sci/? Serious question, visitor from other boards here.
His theories opened new doors for astrology, especially in blackholes. Nowadays he's just getting paranoid about AI, as he thinks his wheelchair is gonna stab him in the back.
>>7795963
>astrology
kek
>>7795928
I'm pretty sure almost all of his work are various theories on black holes.
>muh Quantum Entanglement!
>muh Quantum Computation!
>muh Quantum Teleportation!
>muh Quantum Graviton!
Memes aside, has there been any recent HARD experimental evidence of Quantum mechanics besides mathematical simulations?
>inb4 hurr durr double slut experiment because thats 100 years old
Why are you asking questions about quantum on a science board ? This isn't bed time stories you know.
As of today, the new largest prime number we know of has been confirmed of being [math] 2^{74,207,281}-1 [/math]
It is the 49th Mersenne prime and is 22,338,618 digits long
>>7795758
And?
>>7795769
/thread
mathfags still trying to prove their field is useful
>>7795781
>science and math board
>OP posts thread related to math
Im guessing you're failing your civil engineering courses right OP?
![link-fate[1].jpg](https://i.imgur.com/Zon2cPZ.jpg "link-fate[1]")
![sM835PD[1].gif](https://i.imgur.com/B6gICsj.gif "sM835PD[1]")
