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 …

Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was considered i...

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, …

The argument seems to hinge on whether one is to define 0^0=1 and economize several definitions and theorems from algebra, combinatorics, and analysis, at the expense of one caveat for a single …

A 0 0 -form on a vector space is just a scalar. A 0 0 -form on a manifold is a function (i.e. it assigns a scalar to each tangent space of the manifold).

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 …

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 …

Oct 9, 2013 · Is a constant raised to the power of infinity indeterminate? I am just curious. Say, for instance, is $0^\\infty$ indeterminate? Or is it only 1 raised to the infinity that is?

93 The other comments are correct: 1 0 1 0 is undefined. Similarly, the limit of 1 x 1 x as x x approaches 0 0 is also undefined. However, if you take the limit of 1 x 1 x as x x approaches zero from the left or …

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