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  • State whether the given statement is true or false? Justify your answer by an example. There are infinitely many integers between any two integers.

State whether the given statement is true or false? Justify your answer by an example. There are infinitely many integers between any two integers.

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best_answer

Answer: False

Solution.

An integer is a number which can be written without fractional components or decimal representation. They can be positive, negative or zero.
Examples: \left \{ .....-4,-3,-2,-1,0,1,2,3,4,..... \right \}
The given statement is “There are infinitely many integers between any two integers.”
This is false, because between two integers (like 1 and 9), there does not exist infinite integers.
Also, if we consider two consecutive integers (like 8 and 9), there does not exist any integer between them.
Therefore the given statement is False.

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