I absolutely LOVED this idea. My only complaint is that it's really easy to be put in an impossible level, especially the first level.
Viewing post in Enter the Classroom jam comments
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.
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.