There is more below.
Ниже есть продолжение.
We review the extended rational numbers, which extend the rational numbers to all expressions of the form a/b, where a and b are integers---even b=0. Then we give some examples of how these strange beasts might prove useful in mathematics. But first we give one example of where they are unlikely to be useful---in economics, where there is a big difference between a very big positive number and a very big negative number!https://www.youtube.com/watch?v=YMQkLojL2ek
When we graph rational polynumbers, we see situations where the graph seems to want to ``go up to infinity'' and then immediately ``come up from infinity''. This suggests to us that the mathematics wants us to connect these seemingly divergent arms of a graph, by introducing a point at infinity. We give some initial suggestions that this might allow us to compactly visualize the entire graph of a rational polynumber on a finite square with opposite sides identified. Topologically this is a torus, so perhaps studying infinity will naturally lead to calculus being more naturally visualized, at least for some problems, on a donut!