Real Analysis Answers

Dear Expert sir i have anohter question.give me an example of a sequence which is both geometric as well as arithmetic.a lot of thanks .

Show that a set can't be a neighborhood of its supremum.

A cafeteria offers a complete dinner that includes one serving each of appetizer, soup, entrée, and dessert for $6.99. If the menu has four appetizers, four soups, seven entrées, and two desserts, how many different meals are possible?

Let xn is greater than or equal to 0 for all n belongs to N.
(a) If xn converges to 0, show that sqrt (xn) converges to 0.
(b) If xn converges to x, show that sqrt (xn) converges to xn.

Let f be a function from A into X, and let Y, Z be proper subsets of X. How do I prove
the inverse function of X = A and
the inverse function of (Y') = the inverse function of (Y)"

this is my homework. the gable end of my house fell down. i need to buy some bricks. the bricks come on pallets of 600. note that 5% of the bricks are broken in the building process. how many pallets do i need? the area of the gable end is 38.75m and the area of a brick is 108cm.. help!

Let x_n is in R and suppose that there is an M in R such that | x_n | less than or equal to M for n in N. Prove that s_n=sup{x_n, x_(n+1), ...} defines a real number for each n in N and that s_1>s_2>....

Find an example in which the infinite union of closed sets
1) is not closed
2) is closed.