/sci/ - Science & Math

>>11165631
[math]/ \curlywedge \color{#d4416d}{\rlap{\,\blacksquare}{\blacklozenge}}\,\llap{\color{#d4416d}{_{^\blacklozenge}^{_\blacklozenge}}\llap{\color{#89112d}{\bullet}}}\!\!\color{white}{^\bullet} \,_{\smile\!\smile}\; \color{#d4416d}{\rlap{\,\blacksquare}{\blacklozenge}}\,\llap{\color{#d4416d}{_{^\blacklozenge}^{_\blacklozenge}}\llap{\color{#89112d}{\bullet}}}\!\!\color{white}{^\bullet}\curlywedge\backslash \qquad\color{#d4416d}{\textsf{
That's not how it works, you little shit}}[/math]

>>9992877
You are obvious proof that evolution is not making humans better and smarter authomatically

>>9689135
Because second law of thermodynamics, also possibly dark energy.

>>8872871
>Seems to me, there should be a certain density (or heat) at which entropy tears apart sub atomic particles, converting all mass into energy.

>>8563164

>>8547379

>>8453325
>Since AB=A and BA=B, A and B must both be nxn in size.
>So A=B=I or A=B=0
No.
Counterexample: A = B = any idempotent matrix other than 0 or I.

>>8427925

>asking for evidence that something didn't happen

>>8421783
>a + b = c
>therefore (-1/a) + (-1/b) = -1/c

>>8417551
>There are millions of these

NO THERE ARE NOT.

We didn't evolved from any currently living species. We had common ancestor who extincted long time ago. Both humans and chimpanzees evolved in different way. Monkeys didn't suddenly stopped evolving while we evolved from them, this is not how evolution works.

>>8108388
>[math]P(A \cap B) = P(A)P(B)[/math]
So you're just assuming that A and B are independent of each other?

>>7945447
>In a social setting, you can have intellectual discussion but it can never go any deeper than whatever comes off the top of everyone's head
>discussion
>round-robin memeing
>discussion
>intellectual

>>7750545
>Infinite values have no physical meaning
>so the answer can't be infinite
Fucking physicists

>>7562765

Pauli's exclusion principle is a consequence of second quantization. Antisymmetrized field operators that anticommute at identical times will follow the Fermi-Dirac statistics. This means that antisymmetric wavefunctions with a single permutation of the coordinates will pick up an overall minus sign, and that superposition dictates that the probability of identical antisymmetric wavefucntions with an odd number of permutations of the coordinates at equal times must vanish.

Let A_n be the set of reals in [0,1] whose base-2 expansion contains at most n digits:

<div class="math"> A_n = \left\{ \sum_{i=1}^n \frac{d_i}{2^i} : d_i \in \{0, 1\} \right\}</div>

Since each A_n is finite, it's Lebesgue-measurable with <span class="math"> \lambda(A_n) = 0[/spoiler].
Also, <span class="math"> A_1 \subseteq A_2 \subseteq \ldots[/spoiler].
Hence
<div class="math"> 1 = \lambda( [0,1]) = \lambda \left( \bigcup_{n=1 }^\infty A_n\right) = \lim_{n \rightarrow\infty} \lambda (A_n)</div>
<div class="math"> = \lim_{n \rightarrow\infty} 0 = 0</div>
Where am I going wrong?

>>6729534

I've heard that "reversing entropy is equivalent to time travel". But is there a physical meaning to this statement, or is it just a symbolic consequence of the second law of thermodynamics?

For example, suppose I found a magic pair of socks on a sidewalk, such that the left sock always has a higher temperature than the right sock, no matter what I do to it. Using my permanent heat gradient to do infinite work doesn't appeal to me, and I'd like to 'travel back in time', whatever that entails. How would I go about this?

Suppose I have a family of sets <span class="math">\{A_i\}_{i\in I}[/spoiler], with union A. I want to find a way of 're-partitioning' A into the same number of sets <span class="math">\{B_i\}_{i\in I}[/spoiler]. Ideally, I'd like some sort of bijection between the two.

If the indexing set I is well-ordered, this SHOULD work: <span class="math">B_i=A\backslash A_i^\ast[/spoiler], where \ is the set difference and <span class="math">A_i^\ast=\bigcup_{j<i}B_j\cup\bigcup_{j>i}A_j[/spoiler]. But I'm lacking the knowledge of set theory to verify it. And I can't help but wonder if there's a way to do this 're-partitioning' if we drop the well-ordered assumption.

tl;dr How do I partition an arbitrary family of sets?

pickrelated

also check http://en.wikipedia.org/wiki/Lotus_feet