Question

Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition or description with a graph or an algebraic example.
A sequence of real numbers, including the meaning of a term of the sequence.

Short answer

A sequence of real numbers is a function from the set N of natural numbers to the set R of real numbers. For example, A sequence$\left(a_n\right)\mathrm{with}{a}_n=\frac{1}{n}\mathrm{for}\mathrm{all}n\in N$

Step-by-step solution

Step 1. Given Information

The given statement is a sequence of real numbers, including the meaning of a term of the sequence.

Step 2. Explanation

A sequence of real numbers is a function from the set N of natural numbers to the set R of real numbers. If $f:N\to R$is a sequence, and if $a_n=f\left(n\right)\mathrm{for}n\in N$, then we write the sequence f as$\left(a_n\right)\mathrm{or}\left(a_1,a_2,...\right)$

A sequence of real numbers is also called a real sequence.

For example, A sequencerole="math" localid="1649142506662" $\left(a_n\right)\mathrm{with}{a}_n=\frac{1}{n}\mathrm{for}\mathrm{all}n\in N$