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Check whether the set of integers is countable or not.
Prove that a non empty finite set S which is a subset of R contains its infimum
Four relations a to d are defined on sets A and B. Which of the relations represent a function from A to B?.
a. f1 and f2
b.f1 and g1
c. f2 and g1
d. f2 and g2
Let {bn} be a sequence such that bn = 1 + (1/n). Prove that inf(bn) = 1
using delta - epsilon definition prove that lim(x-->0) (sinx/x) = 1
solve the given question shortly
Q. Find all metric on a set X consisting of two points.
Q. Prove shortly that normed linear space is also a metric space.
solve the given question shortly
Q. Show that another metric D on a set S is defined by d(x,y)=∫_a^b▒〖|x(t)-y(t)|dt〗
solve the given question shortly
Q. If A is a subspace of l^∞ consisting of all sequence of 0 and 1. What is the induced metric on A?
Q. Let D be a metric on X determined all constant k.
Prove shortly that k+d is a metric.
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