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this post was submitted on 23 Oct 2023
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Asklemmy
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This clicked for me when my teacher explained it in terms of slopes.
The video here breaks it down nicely. https://virtualnerd.com/sat-math/geometry/slope/infinite-slope-definition.
So you have a vertical line with an infinite slope. There are no changes in x as you traverse the line, only changes in y. Or said differently, the line is described entirely by a single x-value which corresponds to every possible y-value.
If you think of it in terms of a function, it's extremely problematic because you no longer have a mapping of a single y-value to each x-value. This violates the requirements of a function. It's not possible to define the slope value when rise/run is something/zero, therefore we describe the function value as "undefined".
But even though we can't calculate a slope or address it with a function, it's pretty easy to visualize and understand a vertical line. So that's what dividing by zero represents in concrete terms.