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The question really is that simple Start asking to get answers find the answer to your question by asking Prove that the manifold $so (n) \subset gl (n, \mathbb {r})$ is connected

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It is very easy to see that the elements of $so (n. The generators of $so(n)$ are pure imaginary antisymmetric $n \\times n$ matrices I'm in linear algebra right now and we're mostly just working with vector spaces, but they're introducing us to the basic concepts of fields and groups in preparation taking for abstract algebra la.

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If he has two sons born on tue and sun he will mention tue

If he has a son & daughter both born on tue he will mention the son, etc. Also, if i'm not mistaken, steenrod gives a more direct argument in topology of fibre bundles, but he might be using the long exact sequence of a fibration (which you mentioned). I am really sorry if this answer sounds too harsh, but math.se is not the correct place to ask this kind of questions which amounts to «please explain the represnetation theory of so (n) to me» and to which not even a whole seminar would provide a complete answer 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. The son lived exactly half as long as his father is i think unambiguous

Almost nothing is known about diophantus' life, and there is scholarly dispute about the approximate period in which he lived.