Why is the size of a list less than the size of the objects that comprise it?
How do I determine the size of an object in Python?
I can't retrieve my Facebook password I haven't been to my Facebook account in a while and I can't remember my password. When I try to have it reset, it goes to a security question, but I can't remember that either.    Is there anything I can do? $X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$. This is a problem in KaiLai Chung's A Course in Probability Theory.     Given a nonnegative random variable $X$ defined on $\Omega$, if $\mathbb{E}(X^2)=1$ and $\mathbb{E}(X)\geq a &gt;0$, prove that $$\mathbb{P}(X\geq \lambda a)\geq (a-\lambda a)^2$$   for $0\leq\lambda \leq 1$.   Let $A=\{x\in \Omega:X(x)\geq \lambda a\}$, we get $$\int_A (X-\lambda a)\geq a-\int_A\lambda a -\int_{A^c}X$$ and $$\int_A (X^2-\lambda^2 a^2)=1-\int_A\lambda^2a^2-\int_{A^c}X^2$$ I want to contrast $\int_A (X-\lambda a)$ and $\int_A (X^2-\lambda^2 a^2)$, but I don't know how to do it, could anyone gives me some hints? Unable to solve equation for a variable by any method How do  form? Why are they called the "time-reversed" versions of a black hole? What's an "eternal" black hole? How come a white hole is only encountered if you remove the star from the space-time surrounding the black hole? Why is it that if you add any matter to the area that the white hole disappears? Any explanation greatly appreciated. Meta's tag pages inaccessible due to self-redirect loop Is there any term used for multiple hat tricks? If a bowler takes more than three sequential wickets (say six wickets) in one over, would this be called as two hat-tricks or does this feat, however unlikely, has a different name? So I'm using an app that stores images heavily in the DB. What's your outlook on this? I'm more of a type to store the location in the filesystem, than store it directly in the DB.  What do you think are the pros/cons? Is a string literal in c++ created in static memory and destroyed only when the program exits? I have interesting bug that I have experienced before but has gone away on its own. This one is not going away though.  I have a giant stripe or chunks missing from my desert biome, I would say probably 7 chunks long.  I'm guessing the chunks are corrupted or something, what was hoping to figure is whether it can repaired or reverted.  Here is a picture of the problem. Would approaching a distant star at near the speed of light unfold its entire history in "fast-forward"? What is a field, really? Last two digits of $3^{400}$ Where did the "Magic Blood" of the Harry Potter Universe Originate From? What is a wizard that makes them non-Muggle? Or, more directly, what ancestry does the witch/wizard gene follow? Is there a patriarchal wizard (or matriarchal witch) that Muggles have no part in? Elves perhaps? Stop reading here.  Purpose of the Question/History/Don't Read There seem to be solid consequences associated with being Muggle, or Muggle-related. A dominant theme in the novels is discrimination against the non-gifted race, but, when read into, the wizard bloodline doesn't appear all that well defined. JKR indicates that wizard-ness is genetic, or inherited:  &quot;Muggle-borns will have a witch or wizard somewhere on their family tree, in some cases many, many generations back. The gene resurfaces in some unexpected places.&quot;  By the above, it stands that a family that produces a squib (non-magical born of magical parents) must be a half-blooded family in some way, since half-blooded only requires one non-magical ancestor. Of course, we are dealing in magic genetics. Any other form of genetics would make this inherited, seemingly recessive trait (or squibs couldn't exist), never appear at all. Unless they were XMen. If it is so important, what does the wizard-bloodline follow? Other Mythos In other literature a wizard can be nearly anything, but magical powers are typically inherited as well as learned. Merlin of the Arthurian Legend (also mentioned in HP) is Cambian, meaning he is born of demonic intervention; this explains his source of enchantment. Gandalf of Middle Earth is a Maiar, as are all Wizards of Middle Earth. Wizards in Harry Potter seem to follow a bloodline, and it has been mentioned (in the question Gabe linked) that genetics have a heavy play in it, meaning that squibs and parents of Muggle-born wizards should have identical genetics. This bloodline must come from somewhere. Magical Creatures In Harry Potter it is common for magical creatures to &quot;mingle&quot; with humans, these beings are typically somewhat magical. Elves have been described to have very strong magic, but are for some unreasonable reason subservient to humans. I may be mistaken, but believe it was hinted that elves and the wizarding lineage had intersected at one time. Maybe I'm imagining this. Genocidal Allusions Voldemort hates muggles, and half-bloods, and whatever else is non-wizard. The presence of this theme, suggests that this wizardly bloodline must be at least defined if the main antagonist is so obsessed with keeping that mysterious bloodline pure. Since Slytherin himself was said to be a supremacist (circa a really long time ago) it suggests that this bloodline should have existed long before he was around, especially if he founded a school with people he was not related to, but were also magical. How can I cite a range of papers, the output is a range of numbers, instead of a list of numbers? In other words, when I type  ... some dummy text here is due to me \cite{me1, me2, me3, me4} ...   I want the output to be     ... some dummy text here is due to me [3-6] ...   instead of     ... some dummy text here is due to me [3.4.5.6] ...   (I use LaTeX, and am currently using the amsart class and whatever it includes. But I am open to other suggestions.) Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$ Question 1: For $n \in \mathbb{N}$ explain why $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$   We must show that it is normal and separable.   $\mathbb{Q}(\zeta_n)/\mathbb{Q}$ is normal since it is a splitting field for $X^n-1 \in\mathbb{Q}[X]$ (I think... Is this correct?).  It is separable because it is of characteristic $0$  Question 2: $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$  Is this because the primitive nth root of unity $\zeta_n$ acts as a generator for a cyclic group? I am unable to fill out a decent proof on this.   Thanks for your help Etymology of "dong" and "dongle" Dong as in ding-dong is clearly onomatopoetic as confirmed by :     ding dong        imitative of the sound of a bell, c.1560.   and similarly for :     ding (v.)       1819, "to sound as metal when struck," possibly abstracted from ding-dong, of imitative origin. The meaning "to deal heavy blows" is c.1300, probably from Old Norse dengja "to hammer," perhaps also imitative. Meaning "dent" is 1960s. Related: Dinged; dinging.   What, then, is the origin of dong to mean penis? Etymonline.com is  here:     dong (n.)        "penis," 1891, of unknown origin.   We also have a much more recent word, dongle, which has no entry at etymonline.com but  claims it is:     Apparently from dangle.   This leads me to the theory that the anatomical and onomatopoetic dongs  are not related and that the former usage, like dongle, derives from dangle. So, my questions are:   Is that so? Does dong (penis) derive from dangle? Sounds reasonable enough but I have found no definitive sources for it. Does dongle derive from dangle? It makes perfect descriptive sense for dong but the USB devices called dongles do not dangle but instead protrude quite rigidly, so I feel that dongle being derived from the cruder meaning of dong makes more sense. Why is the Association Bonus ignored when trying to answer a protected question? I registered on  only to post an answer to .  However, since it's a protected question, I am not allowed to answer it. (I found this info from ).  Worth to mention, I can comment on the above question, just not post an answer.  I was under the impression that the whole point of association bonus was to bypass such limits, so why isn't that the case for answering protected questions? No surname in my passport Why is it not true that if $\Phi \models \exists x \phi$ then there is a term $t$ with $\Phi \models \phi \frac{t}{x}$? I got a positive definite matrix $B,$ that is, $V(x) = x^TBx &gt; 0$ for any vector $ x \neq 0.$  I want to show that $ \lambda_\min \|x\|_2^2 \leq V(x) \leq \lambda_\max \|x\|_2^2$ for any $x \neq 0,$ where $\lambda_\min$ and $ \lambda_\max$ are defined by $$ \lambda_\min = \min \lbrace | \lambda|: \lambda \text{ is an eigenvalue of } B \rbrace$$ and  $$ \lambda_\max = \max \lbrace | \lambda|: \lambda \text{ is an eigenvalue of } B  \rbrace$$  Any hint please?