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Welcome to the language barrier between physicists and mathematicians Here in the question it is not stated that the couple has exactly 4 children Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators

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I have known the data of $\\pi_m(so(n))$ from this table What's wrong with my reasoning What is the fundamental group of the special orthogonal group $so (n)$, $n>2$

The answer usually given is

To gain full voting privileges, The generators of $so(n)$ are pure imaginary antisymmetric $n \\times n$ matrices Yes but $\mathbb r^ {n^2}$ is connected so the only clopen subsets are $\mathbb r^ {n^2}$ and $\emptyset$ In case this is the correct solution

Why does the probability change when the father specifies the birthday of a son A lot of answers/posts stated that the statement does matter) what i mean is It is clear that (in case he has a son) his son is born on some day of the week. I'm not aware of another natural geometric object.

U(n) and so(n) are quite important groups in physics

I thought i would find this with an easy google search What is the lie algebra and lie bracket of the two groups? What is the probability that their 4th child is a son (2 answers) closed 8 years ago

As a child is boy or girl This doesn't depend on it's elder siblings So the answer must be 1/2, but i found that the answer is 3/4