Genady

Yes. Gravitational waves.

He asked about (my emphasis) Edit: x-posted

I understand that they ask about, in this case, P(y(x) < 0), which is in [0,1]. Example: y(x) = x2, on [0, 10]. What is probability of y to be within [36, 64]? For x2 < b, x < sqrt(b). So, P(36<y<64) = (8 - 6)/10 = .2

If you can solve inequality y(x)<b, then the range of x in this solution over x1-x0 gives you probability P(y<b). The probability P(a<y<b)=P(y<b)-P(y<a).

Because they hit you sometimes, or something else?

Thank you. Yes, this is new to me, although it is not surprising as my course of set theory was quite basic. But why did you call these solutions "not altogether satisfactory"?

Thank you. Here I've sketched it. The four shapes are 1-0, 2-0, 3-0, and 4-0, where I've numbered the opposite vertices of each:

ChatGPT asked me to tell you this: Just passing the message 😉

In addition to very good questions above, what does it mean to prove a theory? Is there a proof of any theory in physics that you can point to?

Two triangular pyramids, not necessarily equilateral, attached at a base make a shape with triangular faces and nine edges. Trying to imagine how to put four of these shapes together.

What are you talking about?

I do. One. I saw how a person was misdiagnosed with bipolar disorder. (Unfortunately, it turned out to be something much worse.)

Yes, this is right. One syntax might be preferred over another, depending on a context. For example, to the question, what bites the man? the preferred answer would be, cheloveka bites dog. Exactly.

I think that I've answered what @TheVat was referring to, judging by his following up.

Almost. What is modified in Russian in this case is the object noun. 'Man' = 'chelovek'. But 'dog bites man' = 'dog bites cheloveka'. All six permutations are grammatically correct and mean the same, with a different emphasis: 'dog bites cheloveka' 'dog cheloveka bites' 'bites dog cheloveka' 'cheloveka dog bites' 'bites cheloveka dog' 'cheloveka bites dog'

A seasonal sport, watching developing storms. This one, the #1 in the image, is quite close to the equator, but I bet it will miss us anyway.

I know many people who don't suffer from the bipolar disorder but are as well capable of generating a new speculation every 10 minutes. They just don't get excited by this activity.

Kay Redfield Jamison - Wikipedia has written about her own bipolar disorder as a professional psychologist working on this illness.

The following example proves that your formula is incorrect. Take v=.8c, u=-.8c. Plug them into your formula. It gives, u'=1.28c which is faster than the speed of light!

Nope. Insight into the workings.

Model organism - Wikipedia:

"A model": we can investigate existence of mathematical objects and then use this knowledge as basis of the investigation in other realms. It is similar to the use of "model organisms" in biology.

To troubleshoot a computer, you don't just observe its misbehavior. You do something and check responses. IOW, you make experiments and collect data.

Of course. But to make a next step, more data are needed.