Hi, I've got a grammar question. 1) "f is such a function that f(0)=0" vs. 2) "f is a function such that f(0)=0". It seems that "such that" is used much more than "such a ... that". Is only 2) correct or is 1) also fine?
Can you please explain the constant of integration that occurs when we partially integrate a function? I'm unable to understand how that constant is a function with respect to other variables except the one with which we integrating .
I am trying to see, when $f( \overline A)= \overline {f(A)}$ is. I couldn't rule out the case that the sufficient condition is that closure of $\overline A$ is compact. Any ideas, counterexamples?
If $\overline{A} \subset X$ is compact, then $f(\overline{A}) \subset Y$ is compact (continuous image of a compact space). If $Y$ is Hausdorff, then as compact subspaces of a Hausdorff space are closed, $f(\overline{A}) = \overline{f(\overline{A})} = \overline{f(A)}$ by what SemiC linked. So it in fact holds.
But consider $Y$ to be the Sierpinsky two-point space $\{0, 1\}$ with topology $\{\{\}, \{0\}, \{0, 1\}\}$. Let $f : [0, 1] \to \{0, 1\}_s$ be the map which sends everything to $0$.
Take $X = A = [0, 1]$. Closure of $A$ in $X$ is $A$ itself which is compact, but image is $\{0\} \subset \{0, 1\}_s$, a subspace which is not closed. It's closure is all of $\{0, 1\}_s$
@Knight If you integrate with respect to $x$, holding $y$ and $z$ constant, say, then the constant of integration may be different when $y$ and $z$ vary (it's a "constant" of integration only so far as $x$ is concerned). Thus, the constant of integration is actually an arbitrary function of $y$ and $z$.
@BalarkaSen They chose it to be studied, but what if they analyze it for weeks and in the end the conclusions are "nah you know what, this was a mistake, the song sucks"
that gives rise to a hyperelliptic curve covered by two affine charts. the first is the one specified, and the second one is $w^2=v^{2g+2}p(1/v)$ subject to the glueing maps $(x,y)=(w/v^{g+1},1/v)$.
Semi, do you appreciate the current researches that are going on in QM? I mean they seem to be more like an engineer than Physicists, they don’t focus on fundamental principles rather they are working on some specific behaviour of some specific substances. Like the potentials of Silicon crystals, analysing the behaviour of helium plasma and what not.
shrug I dunno. "fundamental developments" aren't that interesting to me. i'm more interested in figuring out what neat things nature can do with the theories we understand, than endlessly speculating about what is 'fundamental' in nature
particularly given how unproductive that seems to be at the presentn moment in history
Semi, what’s the fundamental difference between the Engineering course and B.S. courses. Because anyone with engineering Compter Sc. have to have study higher mathematics
Someone at a lunch about a year ago (who wasn't an expert in computer science by any means) said (and I'm paraphrasing non-faithfully I'm sure) C isn't absolutely reliable, so any theorem-prover that is built on C can't be trusted with absolute certainty. Does that seem like a valid concern to you?
There was a youtube video of a guy commenting on that saying it's complete bullshit and that the chess community need to stop gatekeeping chess and stop being so elitist
Not sure how many useless moves black can play to delay it, but Qc6 restricts the d7 square, and the rook can't move anywhere to stop Ra8 mate, the b7,c7 pawns can't move anywhere useful, and if bxc6 then bxc6 again holds b7 and d7 meaning Ra8 is mate still
There are some positions where a human can tell at a glance "black has a lot of checks but eventually I'll get my king to this square, he'll run out of checks and I can finish my winning attack" while the engine gives a 0 evaluation because it can't compute far enough to see the end of the checks
In the TCEC the game ends when both engines agree that a side has a winning advantage iirc (I don't remember what the exact treshold is, maybe like +/-10)
If there is a move that can be refuted, but only by a crazy 3200 elo tactic stockfish won't play it. If it's playing with contempt it will because it'll assume the opponent won't spot it
it's an attitude i've seen discussed re: card games, where (if you're losing and have no other option) you just have to play as though you'll draw exactly the right card at the right moment
Just yesterday I played a 15+10 on lichess where my opponent blundered a queen on move 13 or so, but he had to make me waste 20 minutes to play it all out
How many arrangements of $A, B, C, D, E, F, G, H$ are there such that $A$
and B are between C and D ?
Attempt : I am trying to solve this problem using simple counting process like first place can be occupy by 6 persons second occupied by 6 and so forth I tried to manipulate remaining one. But ...
i was solving question on arithmetic sequences a doubt I have related to properties of a sequence if i say 1/b+c,1/c+a,1/a+b are in ap and if multiply every term by a+b+c then the terms will become a+b+c/b+c ,a+b+c/c+a,a+b+c/a+b
then does not change the sequence i feel it does not change the of sequence
and the same way if I add -1 to each of the new terms the sequence again won't change, so I get an idea what we can and what we can't do in the numbers ,but i do not have this data in a generalized way
How many arrangements of $A, B, C, D, E, F, G, H$ are there such that $A$
and B are between C and D ?
Attempt : I am trying to solve this problem using simple counting process like first place can be occupy by 6 persons second occupied by 6 and so forth I tried to manipulate remaining one. But ...
