MySQLi Insert() on a non-object
Call to a member function on a non-object
Limit as $x\to 0$ of $\frac{(1+x)^{1/x}-e}{x}$ How do you prove the  from statistical mechanics? To prove entropy will only increase with time? How to prove? Please guide. Catalina not allowing to change read/write permissions despite having SIP disabled Currently Running: macOS Catalina 10.15.1 Issue: Ever since I upgraded to Catalina, macOS is not allowing me to change read and write permissions on system protected files, hence, I am not able to tweak the system as per my likes and dislikes. Steps Tried To Solve The Issue: SIP, always remains . So, no question arises regarding any conflict with system integrity protection. I have also tried to force change the permissions on the system files I want to edit using certain brute force commands, which I can't recall the name of, right now. But, I have tried. As of now, I am still unable to change read and write permissions on system protected files and resources. Does Gentle Repose work on a Circle of Spore Druid's Fungal Infestation Ability? The Circle of Spores Druid feature Fungal Infestation states:  If a beast or humanoid that is Small or Medium dies within 10 feet of you, you can use your reaction to animate it, causing it to stand up immediately with 1 hit point. The creature uses the zombie statistics. It remains animate for 1 hour, after which time it collapses and dies.  Circle of Spore druids also gain access to the  spell, which states:  You touch a corpse or other remains. For the duration, the target is protected from decay and can’t become undead. The spell also effectively extends the time limit on raising the target from the dead, since days spent under the influence of this spell don’t count against the time limit of spells such as raise dead.  There seem to be some good arguments that they cannot work together:  First, Gentle Repose states the target cannot become undead, which would seem to preclude Gentle Repose working on a fungally infested creature that appears to be in some sense raised from the dead. Second, gentle repose states you touch a corpse or other remains - one could argue that using the zombie statistics, the fungally infested entity is neither a corpse or remains, but an undead zombie.  However, there are also some reasonable arguments that they could work together:  First, the Fungal Infestation does not say that the creature is undead or a zombie, but that it uses the statistics of a zombie, which might leave room for a RAW interpretation that the features could work together (for example, it could be considered a fungally infested corpse or fungally raised remains). Second, Gentle Repose says that it extends the time limit of raising the target from the dead and makes reference to spells like Raise Dead, which in flavour are similar to what happens with Fungal Infestation.  RAW, can a player cast gentle repose on a zombie created by Fungal Infestation? TimeSpan to String causing an error Can I set background image and opacity in the same property? How to set scale across all blender objects and keyframes? I have long been confused about this notion. I know that for a statement within a single category, forming the dual statement is just reversing every arrows. But what about a statement concerning several categories and functors between them?   Mac Lane suggests reversing all arrows in all categories and leaving the functors invariant in his book "Categories for the working mathematician" (page 32), but it seems that Mac Lane himself doesn't always follow this discipline (when he states "the dual of Yoneda Theorem", he doesn't reverse the arrows in $\mathbf{Set}$ !) Can anyone give me a formal definition of "dualize a statement in category theory"? Exterior power "commutes" with direct sum I know that for vector spaces $V, W$ over a field $K$, we have the following identity :  $$ \bigoplus_{k=0}^n \left[ \Lambda^k(V) \otimes_K \Lambda^{n-k}(W) \right] \simeq \Lambda^n(V \oplus W) $$ which holds in a canonical way : for $0 \le k \le n$, the maps  $$ \Lambda^k(V) \times \Lambda^{n-k}(W) \to \Lambda^n(V \oplus W), \\ (v_1 \wedge\cdots \wedge v_k,w_{k+1} \wedge \cdots \wedge w_n) \mapsto (v_1 \wedge \cdots \wedge v_k) \wedge (w_{k+1} \wedge \cdots \wedge w_n) $$ factors through the tensor product's universal properties, which gives us a map $\varphi_k : \Lambda^k(V) \otimes_K \Lambda^{n-k}(W) \to \Lambda^n(V \oplus W)$, and since the category of $K$-modules has biproducts, we get a canonical map  $$ \varphi = \bigoplus_{k=0}^n \varphi_k : \bigoplus_{k=0}^n \left[ \Lambda^k(V) \otimes_K \Lambda^{n-k}(W) \right] \longrightarrow \Lambda^n(V \oplus W) $$  What if I replace $K$ by a (commutative ring with $1$) ring $A$? Does this map have a kernel? I know it is surjective (it suffices to "look at it", i.e generators of the codomain are obviously all hit by $\varphi$). I don't know if it helps, but I am working in integral domains. In the field case, this is obvious if $V$ and $W$ are finitely generated, since one can use dimension arguments. I wouldn't mind if the above identity held only in the finitely generated case either. If it worked in general it would be cool though.   Note that when trying to compute the inverse map with the universal property, there seems to be a problem... my guess would have been $$ (v_1 + w_1,\cdots,v_n + w_n) \mapsto \bigoplus_{k=0}^n (v_1 \wedge \cdots \wedge v_k) \otimes (w_{k+1} \wedge \cdots \wedge w_n) $$ and this map is obviously $A$-multilinear, but there is a problem with the alternating property ; I get some terms left. I'm guessing this is the wrong map... if there is one. How should I invest my money as a young graduate in Europe? This is related to this , but that question's answers are 95% tailored for residents of the US, basically recommending to full out the 401k retirement plan and this and that about stock market investments. My question is, are there other types of investments that are good for a young person starting out a career? Pointers:  I live in a welfare state in Europe, so I don't have college debt, (debt of any kind actually). Rainy day funds are much less needed than in the US, since here there is unemployment insurance for at least 18 months. I can probably invest 500€-600€ monthly for something. (The question is what.) I am not looking to invest in my retirement (I am already forced to pay for that out of my salary). I want to maximize my earnings for medium term (5-15 years). I specially want to avoid the typical paradox of (be poor in your 20's,30's,40's and be able to use your money after your 50's). That is not an option for me, I want to use my money for X or Y. But the money used has to be earned from an investment. That is a general rule for me.  For example I want to earn from my investments at least 70k€ after 5-10 years. So I'm guessing this would be a high risk investment, correct? I would like to spend on travel, on courses, on sports etc... But I insist that the money I spend should be a result of an investment not from my salary. Additionally I am not looking to buy a house so I don't want a mortgage. Except if this would constitute a good investment? FYI: this applies to France. But I'd like a general answer so others can benefit. If the question is unclear, a duplicate or off-topic don't hesitate to comment Inconsistency in display of animated avatars It has been discussed previously that animated avatars are disliked because they cause a distraction from the content. However, currently animated avatars are not treated consistently.   On desktop, animated avatars are displayed as a still image, both in posts and on the profile page. On mobile, animated avatars are displayed as a still image in posts, but animated on the profile page.   I'm tagging this  because I'm guessing one of these two is unintended. Either avatars should animate on the profile page on both desktop and mobile, or on neither. (I sincerely hope that we are all agreed there should be no animation of avatars in posts.)  Example animated profile    This appears to animate on mobile, and show a still image on desktop (for myself and for other users who have tried).    I'd also like to hear arguments for and against animating only on the profile page, but the main purpose of this post is to clear up the inconsistency. Reapplying for a UK Standard Visitor visa after a refusal How can an 18 month old be taught that bullying is not ok? He seems to like causing the trouble it brings upon him, and bullying, mean acts also seem to please him. He likes to sit on his younger cousin (my son), push him down, and steal his toys. His parents seem to be at a loss about it, and I don't really have any good suggestions to give. Thanks. $f(z)$ and $\overline{f(\overline{z})}$ simultaneously holomorphic How can I iterate, loop, process, or otherwise do something, with each element from a comma separated list of things?  This question       , and the are already lots of very good answers everywhere. However I think it would also be valuable to have a single reference point where all such alternative techniques are explained in detail, with their advantages and disadvantages discussed.  All of plain-TeX, LaTeX, LaTeX3, LuaTeX, Context, etoolbox, pgffor, etc. answers are invited. Please consider explaining, for example:   How does the command/method deal with whitespace around items? How does the command/method deal with empty/missing items? (e.g. a,b,,c) How does the command/method deal with a trailing comma? Can the command/method work of a list stored on a macro? Is each iteration evaluated globally or on a local group? (i.e., if a command is defined during an iteration, does the command survive the loop?) Do items get expanded or somehow mangled before being processed? What about lists where items are key=value or some other kind of pairs? Does the method work for lists separated with something other than a comma? Any other thing I should know before deciding to use this method? Does $f(x) = f(2x)$ for all real $x$, imply that $f(x)$ is a constant function? If a Continuous function $f(x)$ satisfies $f(x) = f(2x)$, for all real $x$, then does $f(x)$ necessarily have to be constant function? If so, how do you prove it? If not any counter examples? String formatting in Python I want to do something like String.Format("[{0}, {1}, {2}]", 1, 2, 3) which returns:  [1, 2, 3]   How do I do this in Python? How can PCB trace have 50 ohm impedance regardless of length and signal frequency? Hmm, this seems to be just another question on line impedances.  I understand that when we say "transmission line" effects we talk about things like cross talk, reflections and ringing (I guess that is just about it). These effects are not present at low frequencies where the PCB trace behaves like an "ideal" transmission medium, more like we expect a wire to behave in our early school days.  I also understand that the 50&nbsp;ohm value comes not from the line resistance which is going to be very small and less than 1&nbsp;ohm. This value comes from the ratio of L and C on the line. Changing C by changing the trace height above ground plane or changing L by changing the trace width shall change the impedance of the line.  We all know that the reactance of L and C is dependant on the signal frequency as well. Now my questions:   Why should we not call this as line reactance only rather than line impedance? How can it be just 50&nbsp;ohm? It has to be signal frequency dependent right?  E.g 50&nbsp;ohm at 1&nbsp;MHz  Will the world end if I chose to do a 100&nbsp;ohm or 25&nbsp;ohm trace instead?  I know that while we like to say 50&nbsp;ohm as a magic number, it will be within some range around 50&nbsp;ohm and not 50.0000 ohm exactly.  Is there any time when the actual resistance of a PCB trace may matter? For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$ MySQL: How to retrieve a random row or multiple random rows?