Can someone fully solve this for me please
5. (6 marks) For each of the following sets determine whether the supremum and infimum exist and ...
5. Describe the following sets of real numbers and find the supremum and infimum of these sets: (a) {x}\x2 – 2 <4€R} (b) {x|x+ 2 +13 – x4<4} (©) {x|x<for all neN} 6. For any two elements x and y of an ordered field, prove that _x+ y + x- x + y - x - y (a) max{x,y}=- (b) min{x,y}=-
Separate each answer? 5) Define the supremum of a bounded above set SCR. 6) Define the infimum of a bounded below set SCR. 7) Give the completeness property of R 8) Give the Archimedean property of R. 9) Define a density set of R. 10) Define the convergence of a sequence of R and its limit. 11) State the Squeeze theorem for the convergent sequence. 12) Give the definition of increasing sequence, decreasing sequence, monotone se- quence. 13) Give the...
Ctr 6. (20 pts.) For each of the following sets, determine the interior points, the boundary points, the accumulation points and the isolated points.Also deter- mine whether the set is open, closed, or neither (Justify your answer). s= (10,3) n (1,41) u {-1,5} Ctr 6. (20 pts.) For each of the following sets, determine the interior points, the boundary points, the accumulation points and the isolated points.Also deter- mine whether the set is open, closed, or neither (Justify your answer)....
(6 marks) Evaluate the following limits, or explain why they do not exist. You should show your working, but formal proofs are not required for this question. You can assume any results which were proved in class. - i (P) 1,ਜਤ ਘi ( () wਤ 1 tan (੧) + 8 0 II! - % + +
5. (a) (7 marks) Determine whether the following sets form a basis for R3. Explain your answers. i. - {0:0} - {0:00) - {000) -*-**(0-1 1 (b) (3 marks) Is the set W = a vector space? Explain your answer.
6. Decide whether each of the following sets of quantum numbers are allowwed in the hydeogen atom. Briefly explain why they are allowed, or why not a. 3, /2, m -3 allowed not allowed b. 4,/ 3, m0 allowed not allowed 2,/ 2, m+1 c. allowed not allowed 7. Give the maximum number of electrons in an atom that can have these quantum numbers. Show your reasoning. a. 4 b. 3, m, + 2 c. 3,/= 3 d. n 5,/-1...
Question # 1. (6 marks) (a) Determine whether the following integral converges or diverges. L". tan(34) de (b) Determine whether the following integral converges or diverges. 8 dar ſi VE – (2+sin() (c) Consider the function, f(x) = 3-*, by computing each, determine which has a greater value, ſin(81) 5 (7)de or 5f(n)
For each of the following sets a binary operation * is definded. Determine whether this operation defines a group structure on the set. If it does not, specify which axioms fail to hold. 6. Let G be a finite group containing an even number of elements. Show that there must be some elementgEG with gte and g? = e. %3D
1. For each of the two sets of numbers below, determine whether it is a field. If it is a field, just write it is a field. If it is not a field, write It is not a field, state which of the field properties does not hold, and give an example showing this. (a) F = { a+bV2: a,b € Z} That is, F is the set of all numbers of the form a + b2, where a and...
6. (4 marks) Write down the negation of each of the following statements. Then determine whether the statement or its negation is true, and explain why (a) x E R, y E R such that xy 5. (b) z, y E R+ such that V z E Z+, > z.