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 …

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 …

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 …

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 …

11 Several years ago I was bored and so for amusement I wrote out a proof that 0 0 0 0 does not equal 1 1. I began by assuming that 0 0 0 0 does equal 1 1 and then was eventually able to …

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 is undefined. Similarly, the limit of 1 x as x approaches 0 is also undefined. However, if you take the limit of 1 x as x approaches zero from the left or …

Feb 20, 2018 · Under many definitions, 0 0 is said to divide 0 0 and 0 0 is divisible by 0 0. Under some other definitions however, 0 0 is treated as a special case and is considered ineligible to …