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 …

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

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 …

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 …

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, …

You can also prove it by moving the space: "0! = 1" ⇔ "0 != 1", which is computer notation for "0 ≠ 1" :-). Then it depends on what you count as "first principles". If we're dealing with the natural numbers, this …

Nov 8, 2013 · That 0 0 is a multiple of any number by 0 0 is already a flawless, perfectly satisfactory answer to why we do not define 0/0 0 / 0 to be anything, so this question (which is eternally recurring …

@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, …

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 deduce that, …

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 …