It works for me. I often use it.
Just have it tested again. I closed the screen after typing the sentence above, went to another thread, came back - it was here.
Turns out that the sum of squares of the three distances, a2 + b2 + c2, is the same for all points on the circle.
It appears as an algebraic "accident."
What could be a geometric reason for this fact?
All these factors go under the "tired light" hypotheses. They were investigated quite thoroughly, and the general conclusion is that they don't fit observations. There are many articles about them, their predictions and tests. Perhaps other members here will give you more specific answers.
I've found some information on it here: quote source - Who said "Poetry is the art of giving different names to the same thing"? - Literature Stack Exchange
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).
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"?
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