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1d
suggested approved edit on In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$?
1d
comment Is $\frac 1 0$ undefined or equal to $\tilde{\infty}$?
It will if one defines 0/0=0 which is perfectly sane.
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comment Is $\frac 1 0$ undefined or equal to $\tilde{\infty}$?
The limit exists on the affine real line/complex plane.
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comment Is $\frac 1 0$ undefined or equal to $\tilde{\infty}$?
I want to answer this, please reopen.
1d
revised Why these arguments for $\frac 00=0$ are not valid?
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comment Explanation of method for showing that 0 / 0 is undefined
So why one cannot define $0/0=0$? Is having multiplicative inverse of 0 needed for defining this?
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comment Why these arguments for $\frac 00=0$ are not valid?
@Rahul then I am more interested in the second given there are no fatal inconsistencies.
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comment Why these arguments for $\frac 00=0$ are not valid?
@Lucian where I did?
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revised Why these arguments for $\frac 00=0$ are not valid?
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comment Why these arguments for $\frac 00=0$ are not valid?
@Rahul what's the difference of first and second? The third is possibly because it is less useful than taking different limits and does not pop up in practice.
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revised Why these arguments for $\frac 00=0$ are not valid?
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comment Why these arguments for $\frac 00=0$ are not valid?
@JiK it is equal, so?
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revised Why these arguments for $\frac 00=0$ are not valid?
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comment Why these arguments for $\frac 00=0$ are not valid?
@Rahul I do not. The point meant that this is a fundamental properties for all $x\ne 0$ but it can be generalized to 0.
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comment Why these arguments for $\frac 00=0$ are not valid?
@Rahul a·(b+c)=(a·b)+(a·c), take c=0, you get ab=ab+a0, so a0=0. Now take a=1/x
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comment Why these arguments for $\frac 00=0$ are not valid?
@ Ale no, in my definition only 0/0=0.
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comment Why these arguments for $\frac 00=0$ are not valid?
@Yves Daoust this rule anyway cannot be applied or used if b=0. So the chack $b\ne0$ remains, so what?
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comment Why these arguments for $\frac 00=0$ are not valid?
0/0=0 satisfies your condition.
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comment Why these arguments for $\frac 00=0$ are not valid?
@Ale You are confucing $0/0$ with limit $\lim_{x,y\to0}x/y$ The first is not necessary the second. As well as 1/1 is not always equal to $\lim_{x,y\to1}x/y$
2d
revised Why these arguments for $\frac 00=0$ are not valid?
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