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

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...

@Arturo: I heartily disagree with your first sentence. Here's why: There's the binomial theorem (which you find too weak), and there's power series and polynomials (see also Gadi's answer). For all this, …

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 …

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, …

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 …

04 = 0 0 4 = 0 03 = 0 0 3 = 0 02 = 0 0 2 = 0 01 = 0 0 1 = 0 00 = 0 0 0 = 0 Right here, it seems like 00 0 0 can be equal to either 0 0 or 1 1 as proven here. This must be why 00 0 0 is indeterminate. Do you …

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 …

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.

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 …