Practice Finite vs Infinite in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Finite describes a quantity or set with a definite end; infinite describes something that goes on forever without bound.

A jar of 100 marbles is finite. The counting numbers are infinite.

Example 1

easy
Classify each set as finite or infinite and explain: (a) the days of the week, (b) the multiples of 7, (c) the letters in the word 'MATH', (d) the decimal digits.

Example 2

medium
Is the set of decimal numbers between 0 and 1 finite or infinite? Is it countable or uncountable? Justify briefly.

Example 3

easy
For each, say whether the process terminates (finite) or goes on forever (infinite): (a) counting to 1{,}000{,}000, (b) listing all prime numbers, (c) writing the decimal expansion of \frac{1}{3}.

Example 4

medium
A hotel has infinitely many rooms, all occupied. A new guest arrives. Explain (Hilbert's Hotel) how the hotel can accommodate the guest without anyone leaving.
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