安裝中文字典英文字典辭典工具!
安裝中文字典英文字典辭典工具!
|
- Justifying why 0 0 is indeterminate and 1 0 is undefined
So basically, 1 0 does not exist because if it does, then it wouldn't work with the math rules Let τ=1 0 0τ=1 x0τ=x 0τ=x τ=x 0 1 0=x 0 which doesn't work (x represents any number) That means that 1 0, the multiplicative inverse of 0 does not exist 0 multiplied by the multiplicative inverse of 0 does not make any sense and is undefined
- Is $0$ a natural number? - Mathematics Stack Exchange
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 axioms (and a lot of natural number theory does) then you take $0$ to be a natural number
- complex analysis - What is $0^{i}$? - Mathematics Stack Exchange
$$\lim_{n\to 0} n^{i} = \lim_{n\to 0} e^{i\log(n)} $$ I know that $0^{0}$ is generally undefined, but can equal one in the context of the empty set mapping to itself only one time I realize that in terms of the equation above, the limit does not exist, but can $0^{i}$ be interpreted in a way to assign it a value?
- I have learned that 1 0 is infinity, why isnt it minus infinity?
1 x 0 = 0 Applying the above logic, 0 0 = 1 However, 2 x 0 = 0, so 0 0 must also be 2 In fact, it looks as though 0 0 could be any number! This obviously makes no sense - we say that 0 0 is "undefined" because there isn't really an answer Likewise, 1 0 is not really infinity Infinity isn't actually a number, it's more of a concept
- Seeking elegant proof why 0 divided by 0 does not equal 1
The reason $0 0$ is undefined is that it is impossible to define it to be equal to any real number while obeying the familiar algebraic properties of the reals It is perfectly reasonable to contemplate particular vales for $0 0$ and obtain a contradiction This is how we know it is impossible to define it in any reasonable way
- algebra precalculus - Zero to the zero power – is $0^0=1 . . .
Whereas exponentiation by a real or complex number is a messier concept, inspired by limits and continuity So $0^0$ with a real 0 in the exponent is indeteriminate, because you get different results by taking the limit in different ways
- Is $0^\infty$ indeterminate? - Mathematics Stack Exchange
Is a constant raised to the power of infinity indeterminate? I am just curious Say, for instance, is $0^\infty$ indeterminate?
- How do I explain 2 to the power of zero equals 1 to a child
If $2^0$ is any number, it makes more sense to consider that $2^0=1$ than considering $2^0$ as any other numbers (such as $0$) 2 It is more interesting to consider $2^0$ to be $1$ than giving up Some of the other answers provide good ways to convince a child of these facts
|
|
|