This case isn't as exciting as the parallel postulate case; you're not going to get a whole new branch of mathematics, just a change in a lot of formulas/defini

This case isn't as exciting as the parallel postulate case; you're not going to get a whole new branch of mathematics, just a change in a lot of formulas/definitions/notations. The example in the article is the binomial theorem. Another example is the definition of Taylor Series which defines 0! and 0^0 as 1 so that the series come out cleaner. For reference, we use Taylor Series to define e, sin, cos and there's a really nice proof for e^(ipi)+1=0 using the Taylor Series for these three.