eli5: Why haven’t mathematicians invented a symbol for x/0 like they have pi and imaginary numbers?
In: 277
Pi and i are the results of use “solving” polynomial equations which don’t have solutions by inventing one. We also do this to get fractions from the counting numbers.
For example, lets create 5/3 from the counting numbers. We could ask “what is x if 5x=3?” Since no counting number satisfies this, we define a new number 3/5 which satisfies this.
We can similarly create i by asking “what is x if x^2=-1?” Constructing the reals (including pi) is more complicated.
The problem with creating a number 5/0 is any solution to “what is x if 0x=5” breaks a fundamental (very mild lie) algebraic rule: 0y = 0 for all y. If 5 =/= 0, then we have a big problem! The other numbers we invented earlier don’t break any rules, so those are okay.
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