State whether the following statements are true or false? Justify your answer.
(i) There are infinitely many integers between any two integers.
(ii) Number of rational numbers between 15 and 18 is finite.

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Solution

(i) False. Because between two consecutive integers ( like 1 and 2 ) there does not exist any other integer.

(ii) False. Because between any two rational numbers there exist infinitely many rational numbers.

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Similar questions

State whether the following statements are true or false. Give reasons for your answer.

(i) Every natural number is a whole number.

(ii) Every whole number is a natural number.

(iii) Every integer is a whole number.

(iv) Every integer is a rational number.

(v) Every rational number is an integer.

(vi) Every rational number is a whole number.

State whether the following statements are true or false:

(a) The set of all even natural numbers is a infinite set.

(b) Every non-empty subset of has the smallest element.

(d) For each rational number, one can find the next rational number.

(e)There is no largest rational number.

(f) Every integer is either even or odd.

(g) Between any two rational numbers, there is an integer.

\frac{\sqrt{2}}{3}

\frac{p}{q}, q \neq 0

\frac{\sqrt{12}}{\sqrt{3}}

\sqrt{1} 2

\sqrt{3}

\frac{\sqrt{15}}{\sqrt{3}}

\frac{p}{q}

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