Inclusion of $0$ in the natural numbers is a definition for them that first occurred in the 19th century. The Peano Axioms for natural numbers take $0$ to be one though, so if you are working with these …

Why does 0! = 1 0! = 1? All I know of factorial is that x! x! is equal to the product of all the numbers that come before it. The product of 0 and anything is 0 0, and seems like it would be reasonable to …

Feb 6, 2021 · I just got a question while reading permutation. Why 0 is factorial equal to 1?

As for the simplified versions of the above laws, the same can be said for 00 =0 0 0 = 0, so this cannot be a justification for defining 00 =1 0 0 = 1. 00 0 0 is ambiguous in the same way that the number x x …

Aug 10, 2023 · A value of "0" doesn't tell the reader that we actually do know that the value is < 0.1. Would we not want to report it as 0.00? And if so, why wouldn't we also say that it has 2 significant …

Jan 22, 2017 · For example, 0x = 0 0 x = 0 and x0 = 1 x 0 = 1 for all positive x x, and 00 0 0 can't be consistent with both of these. Another way to see that 00 0 0 can't have a reasonable definition is to …

Jan 12, 2015 · 0i = 0 0 i = 0 is a good choice, and maybe the only choice that makes concrete sense, since it follows the convention 0x = 0 0 x = 0. On the other hand, 0−1 = 0 0 1 = 0 is clearly false (well, …

Oct 28, 2019 · In the context of limits, $0/0$ is an indeterminate form (limit could be anything) while $1/0$ is not (limit either doesn't exist or is $\pm\infty$). This is a pretty reasonable way to think about …

May 14, 2015 · 5 We have x0:= 1 x 0:= 1 for every complex number x x. (Notice that this is the only convention which fits into the rules of arithmetic, and there is no need to exclude x= 0 x = 0. Think …

The most brutally simple approach: Write out the curl of a generic F = (Fx,Fy,Fz) F → = (F x, F y, F z), and then take its divergence. The only assumption required is that all partial derivatives commute, e.g.