let A be a non empty subset of IR which is bounded below. show that Let NER. show that x = inf A ift i) az à for all at A and ii) for all exo, there exists at A much that a <+ ε

Q: Give an enumeration procedure for the set L = {ab*a™: n> 1, m >1}.

A:

Q: Let S = {1,2, .., 30} Let A = {25,26, ...,30} - Determine if A is bounded above and find the upper…

A:

Q: Untersection of any point p is of р the Prove that two neigborhoods a neighborhood.

A:

Q: Let Y be an infinite subset of a compact set X c R. Prove Y' # Ø.

A: Y' denotes the derived set of Y i.e. the set of all limit points of Y. We just need to show that any…

Q: Suppose that functions digih. domain that and Jrg we have continuous. i with the some codomain such…

A:

Q: -w #43 Let n», ², a; >0, 5=1,2,... and a₁ + a₂+...+ an = 1 Prove that a, a ₂ 2-92- + 4 + an 2-an 7…

A: We need to prove summation.

Q: Suppose S and T are nonempty sets of real numbers such that for x in S and y in T, we have x < y.…

A: Upper bound: Let A be a non-empty set. Then, a real number s is said to be the upper boundof the set…

Q: Let x be a Yandom Vaveible with Vayaince. If Y- Is-X, then i's finite what cottelatim Yandm the…

A: The correlation coefficient is used to measure the linear association between two variables. If the…

Q: suppose cX) is valued function on such that f?E R Faib] Does it fallows bounded real taib] that…

A: In the given question given that f(x) is a bounded real valued function on [a,b] then we have to…

Q: Let fex) and g(x) be two (Piece - wi'se) comtinuous functions on Intervál caib]. Then if t) ¿gCx)…

A:

Q: Let S be a nonempty subset of R that is bounded below. Prove that inf S= -sup{-s:s∊S}

A:

Q: Find the fowien senies fon | X), -T<X <A

A:

Q: Provide two disjoint nonempty open sets C, D. Is it possible for a function g : R → R to be…

A: A set is a collection of elements like, numbers, objects. The numbers can be called as set of real…

Q: continous real valued function 58) Let f be a that the set inverse image with respect to f of an on…

A:

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: 23. Let A be a non-empty set of positive numbers, which is bounded above and let B = {xe R: 1/xe A}.…

A:

Q: f : A → B is a function, X is a finite subset of Z, and k is a positive integer For each of the…

A: Given: f : A → B is a function, X is a finite subset of Z, and k is a positiveinteger. We have to…

Q: P that the interval [0.1] is not compact in (R.T)

A: In metric space we have heini borel theorm that stats every bounded and closed set is compact in R…

Q: Use Greea's Theorem ond Compute the Counter clock wise cir culotivn of É around the closed urve C .…

A:

Q: Home uork: Let abeQ such that acb. Prove that HxE OK cbx

A:

Q: t BLX,X) denoted set f al incod bounded operates an defined on ow hat fex every TE BLXX) for Hhe…

A:

Q: econd differentioble function and fol-b. Let ļ be a lo) Prove that fu bsinx+a cos x

A:

Q: Let A be a nonempty subset of R that is bounded below. Define the set B = {b: b is a lower bound of…

A:

Q: Suppose that 0 0. Prove that there is an open set O containing E such that 0m* (0) ≤m* (A) and an…

A: The outer measure m* is a way to assign a non-negative value to any subset of the real numbers that…

Q: Suppose f ond 9 are continuous functions on [0. b] ond thand gee)>0 for all x E [0,b]. Prove that…

A:

Q: Suppose f ond 9 are continuous functions on To.b] ond thead gel >0 for all x E [o,b]. Prove that…

A: Using the Concept of Riemann Integration to prove the Given Theorem

Q: 2 Let fi R>R be defined by fc«) = X-3X=10 land let be g cx) = be defined on the 2X +20 ar largest…

A: Given that f,g :R→R define by  f(x)=x2-3x-10        .....(1) and g(x)=2x+20       ....(2) (a) The…

Q: (c) A line in R² not through the origin ax + by sC #0 then &H. :, t is not a ad Umecepsang but…

A:

Q: The relation R=D(x,y): 5x + 4y >= 100)on the set of positive integers is : O a. Reflexive O b.…

A: R={(x,y):5x+4y≥100}

Q: 2) Let a,bE Q such that a<6. Prove that ax <bx.

A: The statements can be proved by analyzing the results from the given statements. The other methods…

Q: Let X = (6,7), and d be the ususal mortric, d(r, y) = |r - yl Gire ezample of a set ACX, to be not…

A:

Q: 3.17 Let A be a subset of R, and let f be a bounded function with domain A. Show that, if BC A, then…

A: Given that A,B are subsets of ℝ andB⊂A. As f is a bounded function in A and B⊂A then fB⊂fA

Q: let f [o2]→Rbe afunction if x<1 fex)= Is f Riemaninteglable? 下くx か

A:

Q: use interediate value theorem o prove that 2cosk -3x=O a- real zero to between O and I

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Let A CR be measurable with m(A) > 0. Prove the following statements: There exists r> 0 such that A…

A: