Below I have provided an example of a checkbox group including a parent checkbox in an indeterminate state. Some of the child nodes in the Tall Things tree are selected and some are not, therefore Tall Things is presented in an indeterminate state:    When the user clicks on the indeterminate checkbox, what should happen? Should the checkbox be checked, or should it be cleared? More importantly, why?
123067
There is a hierarchy of selectable items, let's say a parent and two children. All three items have checkboxes. When both children are checked, the parent's checkbox is also checked. When both children are unchecked, the parent's checkbox is also clear. When only one of the children is checked, the parent is half-checked (color fill or a diagonal inside the checkbox).  This relationship works both ways - the parent's checkbox works as a select/clear all for the children checkboxes.  What should happen when users click the half-checked parent - check or uncheck? Or rather, what factors might influence this decision?
54762
I have this weird object (vascular tree) which is empty inside, but closed from the top and the bottom:  However, it is empty inside, which makes me unable to use boolean on a bigger object (I want to make a hole in an object through which this object will go through). So I thought I should fill it and then try to boolean. But, how do I fill it?  Thank you sincerely.
82301
Intro:  In completing , he presents an experiment (go to 42:44) which leaves me baffled.    Experiment:  (I recommend watching the video; see link above.)   There is a $2$ kg block with 2 identical strings attached to it: one at the top, the other at the bottom. The top string is attached to a "ceiling", and the bottom to a "floor". Professor Lewin "stretches" the system (by pulling on the bottom string) with the block not accelerating. One string snaps.     Prediction:   Initially, the top string has a tension of approximately $20$ N, to counter the force of gravity. The bottom string has no tension at all. Then, when Lewin pulls the bottom string, it gains some tension $n$ N. To counter act the force exerted by the bottom string, the top string exerts now $20 + n$ N. I assume that the string with more force will give out sooner, leading me to conclude that the top string will break.     Results:  (This was conducted by Lewin, not me; see link above.)   Trial 1: Bottom string breaks. Trial 2: Top string breaks. Trial 3: Bottom string breaks.     Additional Notes:  The results don't seem consistent. If I was right, I'd expect all 3 experiments to be right; conversely, if I was wrong, I'd expect all 3 experiments wrong, with one exception: the results are more-less random and one result isn't preferred over the other.    Question:        Why was my prediction incorrect?   Was there a flaw in my logic?   Why were the results inconsistent?
76946
What are recursive triggers? How can we control them, or prevent infinite recursion?  Are these any risks inherent in them, and any limits that we should be aware of?  Please explain with an example.
65331
I noticed what seemed to be a bug in the way the stackoverflow editor handles numbered lists. I did a search on meta for this and it didn't come up, but if it is a duplicate, I'll delete the question.  Consider the following code:  Here are some points:  1. One 2. Two 3. Three  Here are some more points which continue the theme:  4. Four 5. Five   When you actually type this into the text editor, this is the result:  Here are some points:   One Two Three   Here are some more points which continue the theme:   Four Five   In this case, the ordered list resets after the break. This is probably just an edge case (and not necessarily worth fixing), but I ran into the problem today and figured this would be a good place to raise the topic! My workaround was to use back-ticks around the numeral, but then you lose the hanging indent. (ie, 1. One)  Might this be worth fixing? Is it expected behavior? Or am I doing it wrong?
51853
Why does the tree property hold for regular cardinals but not singular cardinals? (I.e. There exists a tree of height $\kappa$ with countable levels and no cofinal branch for $\kappa$ a singular cardinal)
119097
I am seeing a weird indentation for questions loaded via AJAX (i.e., by clicking the n question(s) with new activity link). The following screenshot was taken before I clicked the link:  And this is after the new question was loaded:  A browser refresh resolves the problem (as can be expected). It was tested with Chrome 88 and Firefox 85 on  (Catalina).
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How symmetric is the hierarchy of indecomposable ordinals?   The process of ordinal arithmetic follows a repetitive, inductive pattern from addition to multiplication to exponentiation etc., in which the morphism from one operation to the next looks pretty much the same - in the respect that every step up is an induction beyond the transinfinite limit of the previous operation.  I'm calling this a symmetry.  We have the concepts of additively indecomposable ordinals, and beyond that, multiplicatively indecomposable ordinals etc.  Does this hierarchy enjoy the same inductive symmetry infinitely far in the same way - i.e. to exponentiation, tetration and beyond?  $1,\omega^\beta$ are additively indecomposable (for all ordinals $\beta$).  $2,\omega^{\omega^\beta}$ are multiplicatively indecomposable.  How does this list continue and what does it look like?    It looks like $0^0=1$ and $1^1=1$ but $(n-1)^{n-1}&gt;n\forall n&gt;2\implies $ so the first two exponentially indecomposable ordinals would be:  $2,\omega$  Is it $2,\omega,\omega^{\omega^{\omega^\beta}}$ for all ordinals $\beta$ and so on?  Or does the list of special cases at the start get ever more complicated, and do the power towers just get taller or do they change?  Tetration is a complicated matter (at least over regular numbers) as the orders of exponents matter and the rule to always apply powers from the right isn't necessarily well-justified, so I imagine there's the potential to get into considering Dyck words etc.  How messy does it get?
51434
I have a std::map like this:  map&lt;wstring,int&gt; Scores;   It stores names of players and scores. When someone gets a score I would simply do:  Scores[wstrPlayerName]++;   When there is no element in the map with the key wstrPlayerName it will create one, but does it initialize to zero or null before the increment or is it left undefined?  Should I test if the element exists every time before increment?  I just wondered because I thought primitive-type things are always undefined when created.  If I write something like:  int i; i++;   The compiler warns me that i is undefined and when I run the program it is usually not zero.
123486
I have three different objects A (Grand Parent), B (Child) &amp; C (Grand Child). All the three objects are related by a lookup relationship. Now, there is field on A object, IsActive which is a checkbox and another field IsEligible on object C which is also a checkbox.  Now, if any of the Grandchild associated with A is having IsEligible marked as TRUE, then IsActive on the A's record should be marked as TRUE . If none of the Grandchild records are having IsEligible marked as TRUE, then IsActive should be marked as FALSE.  Parent - A Child  - B1, B2 GrandChild - C1, C2 associated with B1 &amp; C3, C4 associated with B2.  If either of the records, C1, C2, C3, C4, has IsEligible = TRUE, then IsActive = TRUE on A. If neither of the records, C1, C2, C3, C4, has IsEligible = TRUE, then IsActive = FALSE on A.  How can this functionality be achieved?
59805
According to the  :  If the points are labeled sequentially in the counterclockwise direction, then the area is positive, if they are labeled in the clockwise direction, the area will be negative.  Can anyone please explain why the area is negative, with the change in the order of the points? How does this work? I want to know the logic behind this.
70260
I have a bunch of objects in a flat structure. These objects have an ID and a ParentID property so they can be arranged in trees. They are in no particular order. Each ParentID property does not necessarily matches with an ID in the structure. Therefore their could be several trees emerging from these objects.  How would you process these objects to create the resulting trees ?   I'm not so far from a solution but I'm sure it is far from optimal...  I need to create these trees to then insert Data into a database, in proper order.  There are no circular references. A Node is a RootNode when ParentID == null or when ParentID can't be found in the other objects
113421
i have a visualforce page where i displays a grid with checkbox selection for each row in it. The issue is when i select the checkboxes in page 1 and navigate to page 2 and comes back to page 1, the checkbox selection disappears(unchecked) in page 1. i need to retain and display the checkbox selections while i moving across the pages back and forth. How can i fix this? please help.
28620
In Minecraft, to avoid villagers getting confused with breeding mechanics, etc., any group of villagers (i.e. Iron Farm, Villager Spawner etc.) need to be placed >64 blocks away.   Does this apply vertically, or is it to do with Chunk mechanics?
107797
My problem is that I want to give every player on the same height as an area_effect_cloud within a radius of 25 blocks a scoreboard called 'stunned'.  The command for that would look something like this:  /execute @e[type=area_effect_cloud] ~ ~ ~ /scoreboard players set @a[y=~,r=25] stunned 1   But the only problem is that the y=~ is not a thing in Minecraft, does anyone have a solution to this, that isn't 1 or more command block for every height?
80994
What is the etiquette to denote the end of an example or remark? For proofs, it's the QED symbol (white box). I know it's not necessary for everyone, but I would like to use it to break up the text a little. What should I use? A circle or filled box or what?
21128
From : In calculus and other branches of mathematical analysis, an indeterminate form is an algebraic expression obtained in the context of limits. Limits involving algebraic operations are often performed by replacing subexpressions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is known as an indeterminate form.    The indeterminate forms include $0^{0},\frac{0}{0},(\infty - \infty),1^{\infty}, \ \text{etc}\cdots$   My question is can anyone give me a nice explanation of why $1^{\infty}$ is considered to be an indeterminate form? Because, i don't see any justification of this fact. I am still perplexed.