Question

sv.1 set basics - homework score: 12/50 answered: 6/20 question 7 which of the following sets are finite? you may need to select more than one box. {2,4,8,16,...} the set of all triangles the set of words in the oxford english dictionary {5,10,15,...,95,100}

Explanation:

Step1: Analyze first set

The set $\{2,4,8,16,\ldots\}$ is an infinite - geometric sequence with a common ratio of 2, so it is infinite.

Step2: Analyze second set

The set of all triangles has an infinite number of possible shapes and sizes, so it is infinite.

Step3: Analyze third set

The set of words in the Oxford English Dictionary is a well - defined collection with a finite number of words (although very large), so it is finite.

Step4: Analyze fourth set

The set $\{5,10,15,\ldots,95,100\}$ is an arithmetic sequence with a first term $a = 5$, a common difference $d=5$ and a last term $l = 100$. We can find the number of terms $n=\frac{l - a}{d}+1=\frac{100 - 5}{5}+1 = 20$. So it is finite.

Answer:

The set of words in the Oxford English Dictionary, $\{5,10,15,\ldots,95,100\}$