suppose S and T are infinite sets and Φ : S→T is a function that is not onto  have  S and T  the same cardinality? prove (use mapping)

Q: Which of the following functions f has a removable discontinuity at a? If the discontinuity is…

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Q: xy + xy + xy

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Q: Letweden A-(2,-1.1) 8-(3,0.5), an 0-11.4-5) (a, g, 2) are the compose along 1.3 d & fpecycle the…

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Q: Find the norm of each of the following functions on the given interval and state the normalized…

A: we need to evaluate the integral of the square of the function over the interval, and then take the…

Q: Q = log (sin p) P = q cot p,

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Q: 16. If A and B are Hermitian operators and [A, B] = o, then they share 17. It is common to label…

A: If A and B are Hermitian operators and [A, B] = 0, then they share a common set of eigenvectors. To…

Q: (iii) Next let us modify the inner product space by introducing a weight function w(x) e-a and…

A: The normalisation of the function in this inner product space is given by:

Q: Use the identity above to prove that Ã×(B×C) + B×(C×Ã)=Č×(B× Â).

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Q: In considering two operators that correspond to physical observables, if the operators commute, then…

A: If two operators A and B commute, that is, [A,B]=AB-BA=0, then they share a complete set of…

Q: PROBLEM 2. Find the eigenvalues of a Hermitian operator represented by the following matrix: 1 Â = i…

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Q: Do periodic functions, where f (x = 0) = f (x = L), form a vector space? If they do, explicitly show…

A: f(x) is a periodic function with the following conditions f (x = 0) = f (x = L), This time period is…

Q: please provide detailed solution for a to c, thank you

A: thank you

Q: Identify the function as a polynomial, a rational function, an exponential function, a piecewise…

A: Given           f(x) = 7x+2

Q: b) Prove that the following operators are Hermitian 1) Z 2) Lx

A: (1) Z is z component of  position  operator. Since position operator r = (X, Y, Z) is hermitian.…