Forms inside a form with conflicting form actions
Can you nest html forms?
Is there an alternative to Cantor's cardinalities that makes proper subsets smaller than their sets? Cantor defined an infinite set as a set whose subset can be placed in a one-to-one correspondence with its subset. That is, take the set of all natural numbers: {0, 1, 2, 3, 4,...}. From that set, you can form a subset of all even numbers: {0, 2, 4, 6,...}. There is a one-to-one correspondence between both these sets. After all, you can multiply each member in the set of all natural numbers by 2, and you’ll get the set of all even numbers. Because of this one-to-one correspondence, the two sets have the same cardinality, despite the set of even numbers being a subset of the set of natural numbers. This is counter-intuitive to me. How can a subset of a set be as big as the set itself? To make the intuition more concrete, consider the set of multiples of 1,000,000: {0, 1,000,000, 2,000,000,...}. There is a one-to-one correspondence between this set and the set of all natural numbers. So they have the same cardinality. This is really counter-intuitive.  From as far as I can tell, there are basically two axioms at play here:  A1: If all members of set A can be placed in a one-to-one correspondence with all the members of set B, then both sets have the same cardinality.  A2: If set A is a proper subset of set B, then A has a smaller cardinality than set B.  How Cantor defined infinite sets is that he accepted A1 and rejected A2. That is counter-intuitive to me. But mathematicians might say that my intuition is just wrong. So my question is whether we can define infinite sets in another way, i.e. accept A2 but reject A1. That is, the set of even numbers is smaller than the set of all natural numbers, even though both sets have a one-to-one correspondence. If you think this is counter-intuitive because sets with one-to-one correspondence with each other should have the same cardinality, and thus think this is wrong, why can’t I say the same when Cantor accepted A1 and rejected A2? Either way, there is something counter-intuitive and paradoxical.   So, my questions are:   Can we accept A2 and reject A1 for the definition of an infinite set? What arguments, if any, are given for accepting A1 and rejecting A2? According to the documentation  in order to retrieve a list of picklist values for an object we need to pass in a Record Type Id which can be retrieved using the getObjectInfo method.   The issue is that these are both wire functions and I cannot figure out how to chain these methods.  If I try code like the following:  getObjectInfo({ objectApiName: ACCOUNT_OBJECT })             .then(result =&gt; {                 return getPicklistValues({recordTypeId: result.defaultRecordTypeId, fieldApiName: TYPE_FIELD});             })             .then(result =&gt; {                 this.picklistValues = result.data             })             .catch(error =&gt; {                 this.error = error;             });   I get an error      render threw an error in 'c:getpicklistexample' [Imperative use is not   supported. Use @wire(getObjectInfo).]   If I try something like   @track rtId;      @wire(getObjectInfo, { objectApiName: ACCOUNT_OBJECT })     handleResult({error, data}) {         if(data) {             this.rtId = data.defaultRecordTypeId;         }     }      @wire(getPicklistValues, {recordTypeId: this.rtId,fieldApiName: TYPE_FIELD})     picklistValues;   Then it throws an internal server error. Anybody have an idea as to how I could retrieve the record type Id and then call to get the pick list values like the documentation suggests?  FYI my imports are:  import { LightningElement, wire, track } from 'lwc'; import { getPicklistValues, getObjectInfo } from 'lightning/uiObjectInfoApi'; import TYPE_FIELD from '@salesforce/schema/Account.Type'; import ACCOUNT_OBJECT from '@salesforce/schema/Account'; Show that an integer of the form $8k + 7$ cannot be written as the sum of three squares. I have figured out a (long, and tedious) way to do it. But I was wondering if there is some sort of direct correlation or another path that I completely missed.  My attempt at the program was as follows:   A number of the form, $8k + 7 = 7 (mod 8)$. That is, we are looking for integers a, b, c such that $a^2 + b^2 + c^2 = 7 (mod 8)$.   LONG and TEDIOUS way: $$(8k)^2 = 0 (mod 8)$$ $$(8k+1)^2 = 1 (mod 8)$$ $$(8k+2)^2 = 4 (mod 8)$$ $$(8k+3)^2 = 1 (mod 8)$$ $$(8k+4)^2 = 0 (mod 8)$$ $$(8k+5)^2 = 1 (mod 8)$$ $$(8k+6)^2 = 4 (mod 8)$$ $$(8k+7)^2 = 1 (mod 8)$$  That is, using three of these modulo there is no way to arrive at  $$a^2 + b^2 + c^2 = 7 (mod 8)$$ Why my differential equations become True? Can I submit/ArXiv without my advisor? I am being blocked from publishing my work I joined a research group of a faculty member in 201x, and worked with her for three years. During that time, I collaborated with a large hospital to perform research in the domain of medical informatics. I spoke about my research at two conferences; one was a talk, and the other was a poster presentation. My advisor asked me to write up the research in a paper around the second year, which I did. Around the third year, I decided to switch research groups, because of the relationship between me and my advisor going sour, and not having funding from her (I used to work part-time to fund my PhD research).  Once this happened, she withdrew her support from me publishing my paper and ordered that I give up my work to a fellow grad student. I told her, that my manuscript is in its Nth revision, and that I would like to take it to completion as first author. She was dismissive and didn’t offer any comments on my work. I told her, that, should I pass on my work, I would like to discuss authorship issues in advance, which she wasn’t ready to discuss. She ganged up my new advisor against me, and together they forced me to give up my code, results, paper drafts. I had to then leave the university without a degree.  Fast forward couple of years, I receive an email from a student in her lab (the student whom I had to hand over my work to), saying that they are publishing a paper, and have decided I am the fourth author. I read the paper and found out that it uses my experimental setup and design, data collection, and one of the ideas I had presented (the idea wasn’t the main crux of my paper, but I believe it was novel).  I want to   Publish my original draft in ArXiv/BioArXiv, as first author. Request my advisor to cite my work in their publication.    Given how she behaved with me, I know that despite what I am asking for sounds fair, she is likely to object.  I am asking the community: Can I go ahead and ArXiv it without her permission? I could add her as an author, but not take her permission. Also, if you have any other ideas on how to deal with this situation please let me know.  (For the record, this was at a top-10 school in the US in an engineering department). I need help solving this past exam question, the professor posted exam questions with out solutions to last year's exam, I tried reduction of order, however that seemed to complicate things. And then I tried Euler-Cauchy method however I realized that won't work due to the $(2x^2 + 1)y''$.  Given $y_1=x$ is a solution $$(2x^2 + 1)y'' − 4xy' + 4y = 0$$ Find the second solution $y_2$ for equation. Failed to load map. Error contacting Google servers. This is probably an authentication issue Why does Stack Exchange ask for a reload on successful automatic login? I'm looking for an answer considering both technical limitations and user experience.   Does it need a reload from a technical standpoint? I'm a web designer and I'd like to make a custom wordpress theme for my upcoming blog. The template is already made in photoshop but I need a good starting point. I don't have too much experience with Wordpress but I want something that is SEO friendly which I can edit without risking getting poor search results.  I Know about Starkers and that there are other blank themes out there, but are they good for SEO? At the end of the game, both remaining players have a Baron.   The sum of all cards discarded by both players is equal.  Who wins? Can I open a US bank account even if I don't live in the country? Lightning force:createRecord capture redirect after save Is there a way to use force:createRecord but capture the redirect to the newly created record page that occurs after saving the record? Finally, prevent the redirect from completing?  createRecord : function (component) {     var createRecordEvent = $A.get("e.force:createRecord");     createRecordEvent.setParams({         "entityApiName": "Event__c"     });     createRecordEvent.fire(); } I have a Word file which has some Excel plots in it. Unfortunately I lost the original excel plots and the word file is now 'de-linked'.   Is there a way to retrieve the lost data for the plots? Just copying the plot back to Excel does not seem to work, but I can see that the data is still there somewhere, because hovering over a dot on the plot shows the values. Do comic characters sometimes get drawn like the actor playing them? I noticed in Spider-Man's recent cameo in Captain Marvel, he appeared an awful lot like Andrew Garfield who is playing Spider-Man in the recent movie.    Irrelevant of whether it is just my imagination, do some depictions of comic characters morph to be more like an actor who plays them around the time a corresponding movie is released?  By comparison, here is Spider-Man's depiction in the Spider-Men crossover: How should an educational institute woo good faculty? class and private variables Why does default auto.arima stop at (5,2,5)? The function auto.arima in the forecast package of R is a powerful tool to identify the best ARIMA(p,d,q) model for a given data series. In the   of the function, they report the following:  auto.arima(y, d=NA, max.p=5, max.q=5, max.order=5, max.d=2, start.p=2, start.q=2, ...)   According to the above function it seems that, by default, auto.arima tries to find the best model among all the combination having:   p equal or lower than 5 q equal or lower than 5 d equal or lower than 2 order equal or lower to 5, i.e. p + q + d  ≤ 5.   However, why does the default code stops at these conditions? Is there any particular reason why p, q and d should be equal or lower than 5, 5 and 2 and their sum lower than 5? Short story about survivors on Earth after the atmosphere has frozen If  $\mathbb R^*$ and $\mathbb C^*$ be respectively multiplicative groups of non-zero real and complex number then whether $\operatorname{Hom}(\mathbb Z_6,R^*\oplus C^*)$  is  isomorphic to $\mathbb Z_{12}$? or $\mathbb Z_6$? or $\mathbb Z_6\oplus \mathbb Z_2$? What is the Mediator in this Feynman Diagram $q\bar{q} \rightarrow gg$? Let's consider the t-channel version of the process $q\bar{q} \rightarrow gg$. What is the mediator in this case, a $q$ or a $\bar{q}$? Naively, I would have thought a $q$ (as to have one fermion line), but I am not $100 \%$ sure.