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Sure, you can pose it many different ways. But they do not change the mathematical facts I mentioned above. The terms that you obtain...

It is a mathematical fact that the terms that you obtain are included in the constant of integration. So, it is a mathematical fact that...

I think we had a similar thread a couple of years ago. It might be worth searching for it. I don't use hand rules, but remember the...

Ahh, I was speaking of the OP.

With an infinite charge distribution I don’t think that “external” is meaningful. But, yes, if you are using this as an approximation...

If a veridical paradox were not a paradox, would that itself be a veridical paradox?

The horizontal field is arbitrary. It can be of any size, from negligible, to same order, to much larger. Although in this case the OP...

Which is what boundary values are for.

No. I am saying that the important thing is the conditional probabilities. And I am saying that in the regular approach Monty’s...

Yes, it does make a difference. There is a difference between an accidental result of rare luck versus the intentional act of avoiding...

It is important because it changes the conditional probabilities. As a matter of notation, let’s call the door that the contestant...

It isn't paradoxical if you have ever boiled sap to make maple syrup. The raw sap is 2 or 3 percent sugar, depending on the tree. If...

It changes the probabilities because it changes the relative frequencies, which one can calculate. In other words, you play the game...

I can see why this is considered paradoxical. It took me an hour to build a spreadsheet yesterday to do just the basics of the maths...

I haven’t run the numbers for all of the variations that @PeroK describes. But my educated guess is that the optimal decision will not...