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Welcome to the language barrier between physicists and mathematicians Yes but $\mathbb r^ {n^2}$ is connected so the only clopen subsets are $\mathbb r^ {n^2}$ and $\emptyset$ Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators

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What is the fundamental group of the special orthogonal group $so (n)$, $n>2$ It is clear that (in case he has a son) his son is born on some day of the week. The answer usually given is

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I have known the data of $\\pi_m(so(n))$ from this table The generators of so(n) s o (n) are pure imaginary antisymmetric n×n n × n matrices How can this fact be used to show that the dimension of so(n) s o (n) is n(n−1) 2 n (n 1) 2 I know that an antisymmetric matrix has n(n−1) 2 n (n 1) 2 degrees of freedom, but i can't take this idea any further in the demonstration of the proof

I'm not aware of another natural geometric object. Each of 20 families selected to take part in a treasure hunt consist of a mother, father, son, and daughter Assuming that they look for the treasure in pairs that are randomly chosen from the 80 You'll need to complete a few actions and gain 15 reputation points before being able to upvote

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What's reputation and how do i get it Instead, you can save this post to reference later. 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