Drawing some graphs in Cartesian Coordinate system for a College Algebra class, and wondering:
How are graphs even drawable? Considering that the points that make up graphs have infinitesimal size and have measure zero?
2026-04-04 11:19:49.1775301589
How are graphs drawable?
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The point of drawings or other physical models in mathematics isn't to perfectly model the object, but just to produce something that looks close enough that it can act as a visual aid and help develop some reasonably accurate intuition. (Likewise, most mathematical writing is intended to convey meaning to other human beings, which is why theorems and proofs tend to be written in prose rather than in completely formal symbolic notation.)
The fact that the mathematical object — the graph, in this case — doesn't have a perfect physical model has no bearing on whether we can study it mathematically. We don't need to draw a graph at all to be able to study it, and some functions have graphs for which no drawing would be remotely accurate. (For example, the Conway base 13 function is surjective on every interval; in particular, it's discontinuous at every point and unbounded on every interval.)