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 …

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 …

Apr 6, 2017 · Since 0 ∈ R, 0 ∈ R, there is no dispute that 0 0 is a real number. So, by symmetry, it makes sense to also consider 0 0 an imaginary number. (Wolfram Alpha agrees.) Hence, it …

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 …

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 …

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 …

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 …

Exponentiation R ≥ 0 × R + → R ≥ 0 and/or R + × R → R + by limits of the two above choices. This cannot be extended to give a value for 00, because it has no limit for (a, b) → (0, 0). …

Oct 28, 2019 · 0 0 = x 0 0 = x 0x = 0 0 x = 0 x x can be any value, therefore 0 0 0 0 can be any value, and is indeterminate. 1 0 = x 1 0 = x 0x = 1 0 x = 1 There is no such x x that satisfies …

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 …