Finite and Infinite Sets — Practice

Recall / Warm-Up

These problems review set notation you already know.

Which of these is the correct roster notation for the set of the first three counting numbers?

$(1, 2, 3)$

$\{1, 2, 3\}$

$1, 2, 3$

How many elements are in the set $\{a, e, i, o, u\}$ ?

Fluency Practice

Is the set of grains of rice in a full sack finite or infinite?

Finite — but only because a sack is small enough to fit in a room, not because the count actually ends.

Infinite — there are far too many grains to count, so no total could ever be reached.

Finite — you could count every grain and the count would end.

Is the set of all even numbers $\{2, 4, 6, 8, \ldots\}$ finite or infinite?

Finite — even numbers go up in steps of two, so the pattern is regular enough to count completely.

Infinite — after any even number there is always a larger one, so the list never ends.

Finite — there are exactly four elements shown, and no more are implied beyond them.

Which set is finite?

The set of letters in the English alphabet.

The set of all counting numbers.

The set of all points on a straight line.

The set $\{1, 2, 3, \ldots, 20\}$ has an ending number, so it is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . It has ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ elements.

finite or infinite:

number of elements:

Exercises: Finite and Infinite Sets

Recall / Warm-Up

Fluency Practice