Real Analysis

Is there a rational number exists between any two rational numbers.

Which is not true about number zero.

• Even

• Positive

• Additive identity

• Additive identity of zero

A set A is said to be countable if there exists a function f:A→N such that

• f is bijective

• f is surjective

• f is identity map

• None of these

A sequence {s_n} is said to be bounded if

• there exists number λ such that |s_n|<λ for all n∈Z.

• there exists real number p such that |s_n|<p for all n∈Z.

• there exists positive real number s such that |s_n|<s for all n∈Z.

• the term of the sequence lies in a vertical strip of finite width.

A sequence {1/n} is

• Bounded

• Unbounded

• Divergent

• None of these

Let A={x|x∈N and x²≤7}. Then supremum of A is

• 7

• 3

• 0

• does not exists

Is the sequence {n+2/n+1} is increasing or decreasing?

• Increasing

• Decreasing

Is the set of real numbers countable?

• Yes

• No

If a real number is not rational then it is ……………

Which of the following numbers is not irrational.

• $\pi$

• $\sqrt{2}$

• $\sqrt{3}$

• 7