Real Analysis Answers

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.

sir please differentiate between applied and pure mathematics also classify the folowing as applied or pure mathematics.Real Analysis,complex analysis,topology,group theory,mathematical statistics,calculus,function alalysis.best regards

a compact space having no finite sub space of (0,1)

tan invers x is uniformly continious or not ?

Suppose f is continuous on all real numbers and f(c) is not equal to zero for some point c in all real numbers. Show that there exists an interval (a, b) containing c such that f is never 0 on this interval

Suppose that the limit as n approaches infinity of Xn=0. If {Yn} is a bounded sequence, prove that the limit as n approaches infinity of XnYn=0

Consider the set of natural numbers N.Is it possible to build a family of subsets of N such that it's cardinality is continuum and for arbitrary two subsets A and B - A includes B or B includes A?

let S be a subset of R and let it bounded below , show that infimum of S exists
[ hint: let A= -s :={ -s: s∈S} , show that A is bounded above so sup A exists . now show that inf S= -sup A ]