I have downloaded a book about Calculus from MIT OCW. In that book, there is a section "A Thousand points of Light". (You can download the relevant section from here.)
In that section, it is written that the graph of $y=\sin x$ is different from the graph of $y=\sin n$.
However, I cannot understand this thing. Why will the graph of $y=\sin n$ be different from the graph of $y=\sin x$? How can you change a graph by changing a variable in the function? And how have they plotted the graph in the book?
Best Answer
The main difference between your first and second graph is the fact $y = \sin x$ uses $\mathbb{R}$ as its domain and $y = \sin n$ uses $\mathbb{N}$ as it's domain. Furthermore, the points on the second graph are not connected which implies that the second graph is not continuous and via inspection, you can notice that the $x$-axis only has natural numbers.