0 02 0b 3b24be75754496acf38fb8791be55aaf5d3aa0b2af0f4355b72114512d3f7bf2 Fe05d4dae8ccfa6d Youtube

3e3cf1dbaf61a68259e6b528cb3b8b40 Youtube 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 assume that 0! = 0 0! = 0. i'm perplexed as to why i have to account for this condition in my factorial function (trying to learn haskell. 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.

0b2de2679aef43dbb5ce5817d15bf090 Youtube As for the simplified versions of the above laws, the same can be said for 00 = 0 0 0 = 0, so this cannot be a justification for defining 00 = 1 0 0 = 1. 00 0 0 is ambiguous in the same way that the number x x is ambiguous in the equation 0x = 0 0 x = 0. 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, almost —see the discussion on goblin's answer), and 00 = 0 0 0 = 0 is questionable, so this convention could be unwise when x x is not a positive real. This definition of the "0 norm" isn't very useful because (1) it doesn't satisfy the properties of a norm and (2) 00 0 0 is conventionally defined to be 1. But if x = 0 x = 0 then xb x b is zero and so this argument doesn't tell you anything about what you should define x0 x 0 to be. a similar argument should convince you that when x x is not zero then x−a x a should be defined as 1 xa 1 x a.

0 02 05 39c7c2ca537f82faac90e19a411b0857fb53afc2cf0c11a172dc64324d2452e8 Bb29351bf6be1cfc Youtube This definition of the "0 norm" isn't very useful because (1) it doesn't satisfy the properties of a norm and (2) 00 0 0 is conventionally defined to be 1. But if x = 0 x = 0 then xb x b is zero and so this argument doesn't tell you anything about what you should define x0 x 0 to be. a similar argument should convince you that when x x is not zero then x−a x a should be defined as 1 xa 1 x a. In the set of real numbers, there is no negative zero. however, can you please verify if and why this is so? is zero inherently "neutral"?. My daughter is stuck on the concept that $$2^0 = 1,$$ having the intuitive expectation that it be equal to zero. i have tried explaining it, but i guess not well enough. how would you explain the. 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?. How can i prove from first principles that $0!$ is equal to $1$?.

0 02 05 D3f7dd15a28b10599e6fb5d0aaf0e1ce72d6338ef6cd673dbbaa063bf974b671 7c9db4e99b033106 Youtube In the set of real numbers, there is no negative zero. however, can you please verify if and why this is so? is zero inherently "neutral"?. My daughter is stuck on the concept that $$2^0 = 1,$$ having the intuitive expectation that it be equal to zero. i have tried explaining it, but i guess not well enough. how would you explain the. 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?. How can i prove from first principles that $0!$ is equal to $1$?.