- What does i-th mean? - Mathematics Stack Exchange
I have seen a problem set for the tower of hanoi algorithm that states: Each integer in the second line is in the range 1 to K where the i-th integer denotes the peg to which disc of radius i is
- How to prove Eulers formula: $e^{it}=\\cos t +i\\sin t$?
Actually, it is common to define eit e i t using your equation If something is to be proved we must start by asking what we know about the involved parameters, so how is your definition of eit e i t? Do you use a series or some other limit process?
- Is thi set of vectors, $\\{(2, 1), (3, 2), (1, 2)\\}$, is linearly . . .
So, c3 c 3 is the free variable Assuming c3 c 3 is non zero, the vectors are linearly dependent If it is zero, vectors are linearly dependent How can it be that a free variable decides whether vectors are linearly dependent or not ? Shouldn't it a 100% yes or no answer that does not fluctuate depending on values of constants?
- probability theory - Regular conditional probabilities: a confusion . . .
I'm reading a proof of Theorem 2 29 below from this note First, we recall a definition and a lemma, i e , Definition 2 28 Let $(\\Omega, \\mathcal{F}, \\mathbb{P})$ be a probability space, $(T, \\ma
- What is the probability that a device passes the quality control test . . .
The probability that a device passes the quality control test is 0 8 0 8 Find the probability that a given device will pass the test on the third try I don't understand how to go about answering this question It seems to me like there isn't enough information Do I assume each trial is independent? If so, I thought to use the probability distribution of a geometric RV, but this PMF gives
- algebraic topology - Homology of $S^1 \times (S^1 \vee S^1 . . .
I have yet another solution, using cellular homology directly Define a CW-structure on X X with one 0-cell e0 e 0, three 1-cells a, b, c a, b, c, and two 2-cells U, L U, L Attach the 1-cells to e0 e 0 so that X1 =S1 ∨S1 ∨S1 X 1 = S 1 ∨ S 1 ∨ S 1, and attach the 2-cells via the relations so ∂U ↦ aba−1b−1 ∂ U ↦ a b a 1 b 1 and ∂L ↦ cac−1a−1 ∂ L ↦ c a c 1 a 1
- abstract algebra - Why does Lang describe a field as a union and . . .
because E E is clearly contained in the RHS, and each k(α) k (α) is contained in E E and hence so is the union, implying that E E contains the RHS Similarly for point no 6 So, why does Lang emphasise to take the union and compositum over all finitely generated subfields? Is there some perspective that he wishes to emphasise that I am missing? Any help in understanding this will be
- What does open set mean in the concept of a topology?
Often a course in topology starts with metric spaces Then a definition of "open set" arises in that context It can be shown that the collection of these sets has the properties mentioned in def 2 2 and for such a collection a name allready exists: a topology That opens the door to reach out for a more general definition of open set wich is not linked only with metric spaces, but with
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