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安裝中文字典英文字典辭典工具!
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- Justifying why 0 0 is indeterminate and 1 0 is undefined
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 why it is that $0 0$ is indeterminate and $1 0$ is not However, as algebraic expressions, neither is defined Division requires multiplying by a multiplicative inverse, and $0$ doesn't have one
- Why Not Define $0 0$ To Be $0$? - Mathematics Stack Exchange
Limits explain only why it is indeterminate, not why it is undefined $0^0$ is defined to be $1$ even though $0^0$ is an indeterminate form by similar reasoning to your answer
- A thorough explanation on why division by zero is undefined?
Getting Started The other day, I was working on a project at home in which I performed division by zero with a double precision floating point number in my code This isn't always undefined in the computer world and can sometimes result in $\infty$ The reason for this is clearly explained in IEEE 754 and quite thoroughly in this Stackoverflow post: Division by zero (an operation on finite
- What exactly does it mean that a limit is indeterminate like in 0 0?
The above picture is the full background to it It does not invoke "indeterminate forms" It does not require you to write $\frac {0} {0}$ and then ponder what that might mean We don't divide by zero anywhere It is just the case where $\lim_ {x\to a}g (x)=0$ is out of scope of the above theorem However, it is very common, in mathematical education, to talk about "indeterminate forms
- Can you show why zero divided by zero does not equal zero?
So, I said that zero divided by zero then is already zero, and no subtraction ever need take place Therefore the claim is that $\frac {0} {0} = 0$ How can we show that this does not work well? My instructor claimed that there is a smart way of showing how this will not work, but could not remember what it was Does anyone know what it might be?
- Seeking elegant proof why 0 divided by 0 does not equal 1
So if I say 0 0=0, that would be true, and if I say 0 0=1, that would be true as well 0 0=infinity would also be true, 0 0= (-infinity) would be true Think of it like this: nine divided by three is three, because three goes into nine three times But how many times must zero be added to get to zero? If zero is added once, it'll be zero
- Why does 0 0 mean there it a hole and not an asymptote?
It might be zero, it might be infinite, it might be seven, or literally anything else It depends on the specific situation whether you would call a $\frac {0} {0}$ an asymptote or a hole, etc
- algebra precalculus - Zero to the zero power – is $0^0=1 . . .
So we make $0^0$ equal to $1$, because that is the correct number of ways in which we can do the thing that $0^0$ represents (This, as opposed to $0^1$, say, where you are required to make $1$ choice with nothing to choose from; in that case, you cannot do it, so the answer is that $0^1=0$)
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