what mindset is a functioning adult supposed to have?
>>3910154
who cares
lol u never functioned
>>3910154
In the modern world, the mindset of a subservient robot.
teacher or student?
Theorem: Let A be the set of all linear maps between the vector space of human abilities (the base of this vector space is not finite) and the vector space of human behaviours (the base of this vector space is again not finite). Then the following are true:
i) Part of A has cardinality greater than aleph zero.
ii) The kernel of every element of A is the null vector.
The proof is left to the reader as it's trivial.
Corollary: the mindset of a functioning adult is not well defined.
>>3910349
thanks
>>3910353
You're welcome friend.
>>3910349
how would one explain the idea expressed here to a young child in a way they can understand?
>>3910356
I suppose that without the use of such asometimes uselessformality, one could simply say that things are much more complicated than we could ever imagine or try to understand. There is no "best way" to be an adult, in fact there is neither a "best way" to be a human being. Everyone is simply different and must find his/her way of being good with others and at the same time in peace with himself/herself. However, there are some general rules one should follow in order to be "good". Nevertheless, these rules may only be learnt through personal experience.
In summary: being a functioning person is a bit of a bad way to think about life. The term "functioning" itself implies many rules which may be in contrast with yourself. Regardless, the key is, in my opinion, to find the correct equilibrium between what YOU want and what OTHERS need.
Sorry for grammar mistakes. This is just my opinion.
If on the other hand you wanted an explanation about vector spaces, well, it's long.
>>3910364
nigger
>>3910364
i would enjoy an explanation of vector spaces if you would feel inclined to impart your knowledge :)
also: how can an old man become grumpy and rude if his life of learning is a sum of experiences that have taught him the importance of being "good"? - how can one avoid becoming that, and is it necessary to strive to avoid being like that?
nearly got dubs skywalker
>>3910370
That is a good question. I honestly don't know, but I suppose that life changes you in very unpredictable ways. Some people don't question their existence and thus live a much more simple life. This is not to blame, of course, but could lead to perceive reality in a very subjective way (that is, not giving OTHERS enough space in your life). Besides, negative experiences combined with being perhaps inclined to be very negative people could in fact lead to be the grumpy and rude old guy you are referring to. Growing up is a neverending form of learning: you simply never stop meeting new and unexpected things. These will make life worthy of being lived, rather than being rude and wasting your time judging others.
haha the hell if I know lol XD *farts and poos accidenty*
>>3910370
>>3910399
(1/2)
As for vector spaces: a formal definition would probably sound very cryptic, so I'll try my best to give you a general idea. First, a vector space is a mathematical object that arises from adding properties (particular kind of abstract properties) to a set (a set of numbers, cars, people, colours, that is the more abstract idea of set you could have) on which some operations (operations like multiplication, wearing clothes, cooking, that is the more abstract idea of operation you could have) are defined. In Abstract Algebra you start from a set with one operation (abstract operations have a very precise definition) and a few properties (which create a very simple form of algebraic structure), and then you add either operations, or properties or both until you get to very complicated forms (such as vector spaces). Vector spaces are studied both in Algebra and in Geometry. In the latter, they found many interesting applications and have very nice theorems which show the many relations between numbers (in particular, real numbers) and systems that behave like a vector space.
Elements of a vector space are called "vectors" and they are a "rich" structure because you can "do" a lot of things with them. Also, vector spaces are defined on a so called "field" which is itself an algebraic structure on which are defined properties and operations. The simplest field one can imagine is the set F={0,1}, that is the numbers 1 and 0 form a structure which is identical to, say, all real numbers. On a field, a vector space is defined and the elements of the field are called scalars.
>>3910370
>>3910399
>>3910403
(2/2)
Many (physicists, engineers, and so on) study the simplest form of a Vector Space (the one on R^n) called the euclidean vector space. In a two dimensional reality you can imagine it as being "arrows" on a plane, in a three dimensional reality you can imagine it as being "arrows" in the space, and so on. In general, given a n-dimensional reality, a vector space on such a "reality" could be represented by drawing arrows in the n-dimensional space.
(note: although it can be shown quite easily that every vector space of finite dimension n is isomorphic to R^n, it is VERY wrong to think about vector space in terms of arrows).
I would love to give you some weird examples of vector spaces (you can construct one with colours, for instance) but it would require a bit of a more indepth understanding of such structure.
Sorry for wall of text. I love math.
>>3910403
>>3910405
i appreciate that this was shared
>>3910405
can you explain constructing a vector space out of color? (if you are still here)
>>3910464
i forgot to say please c^:
>>3910154
a boring and sucky one
>>3910418
I appreciate that you appreciated it. Math is not only about numbers and calculations, but rather about abstract relations between abstract objects! I find it amusing.
>>3910464
>>3910475
Sure. First, addition between colors can be thought of as literally adding two colors together (for instance, green and blue gives yellow (if I'm not wrong lol)), and one can easily see that the set is closed under such operation. Second, the set of the scalars can be thought of as the set of the various intensity of brightness (this is kind of ill-defined though, but I'm sure one could easily find a better field where to create a vector space, for instance using saturation or other properties of colors; the axioms of the field are easily verified). Then, the properties of addition (associativity and commutativity) are verified; the identity element is white; the inverse is the complementary of a color (these prove that the v.s of colors is an abelian group under the operation of summation). Properties of distributivity are also verified. A basis for such a vector space is the set B={red, green, blue}.
As always, when making such unorthodox examples with complex structures it is easy to find a mistake, but I believe overall this is a good way to at least grasp the concept of vector space. There are lots of other real world examples of different mathematical structures. Algebra is rich under this point of view: having the same ex-girlfriend (or boy-friend) is an equivalence relation; wearing clothes is a non-commutative operation, and so on.
>>3910523
blue + yellow = green
blue + red = purple
red + yellow = orange
is or can time be factored into such equations?
>>3910550
Thanks for the clarification. The point still stands, from the basis you can create every color. I don't understand what you mean by "factored". English is not my first language. If you mean "could we add time in some way to this construction?" then the answer might be yes, even though I'm not sure how.
>>3910554
that's what i meant, and i wonder how it could be added- thank you for the lecture anon /(^_^)7
pic related was me in school tbh, but these days im taking interest in it
>>3910561
Oh then there is surely a way. I'm happy you enjoyed it. This is truly nice board. Now I must go back to check dubs and post dank memes goodbye my friend I love you.
>>3910569
Have you done much analysis?
I am doing complex analysis atm and it is hectic haha
