While most places you look will say otherwise, 0/0 is absolute infinity, people just say it's undefined since it's to complex for elementary school and has like 0 applications. There are a couple patterns that help conclude this, such as when you plot x/1 on a graph you get a diagonal line, then when you plot x/.5 you get another diagonal line, but it's closer to vertical, the smaller the number your dividing by, the closer you get to a vertical line, so 0/0 would be a vertical line. Another pattern that shows this is the graph 1/x, where the lines approach 0, but never get there, just getting closer and closer, because if x=0 then you would get 0/0, but if these lines would eventually hit 0, it would just take the graph past infinity, to absolute infinity.
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There are also a couple patterns that help conclude that 1/0 should be regular infinity and negative infinity.
Namely, the graph for 1/x. Here, as x approaches 0, f(x) approaches both infinity and -infinity, depending on which side you look at.
Furthermore, defining division by 0 as any number yields 1 = 2:
1/0 = absolute infinity = 2/0
1/0 = 2/0 | cancel out the 0
1 = 2
Which is fine since infinity isn't a number.
But it not being a number also means that it is rather nonsensical to represent it in the graph for f(x) since we now have a graph that, for the most part, consists of numbers but then at one point, decides to show a cardinality as a vertical line, which would usually read as "every number at once".
Maybe that is a valid interpretation of absolute infinity but it still means that we're now plotting two incomparable concepts in the same graph for no good reason.