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6h
comment Why Not Define $0/0$ To Be $0$?
you "proved" by multiplying all by $0$. $0$ is a number.
7h
comment Why Not Define $0/0$ To Be $0$?
what you are doing is impossible, it is irrelevant to whether 0/0 is number or not.
7h
comment In dual numbers, what number is represented by the following matrix?
what reasoning do you mean?
7h
comment Why Not Define $0/0$ To Be $0$?
You wrote: $$\frac{1}{1}-\frac{0}{0}=\frac{1\cdot 0-0\cdot 1}{0\cdot 1}$$ - no, you cannot do this, you are multiplying thenomenator and numerator by zero, this does not prove anything (similar way you can prove that 2=1, so 2 is not a number)
7h
comment In dual numbers, what number is represented by the following matrix?
the last matrix is $-i$.
7h
comment In dual numbers, what number is represented by the following matrix?
I have already found it is sometimes denoted $\epsilon'$. Also it seems, it is $i+\epsilon$?
9h
comment In dual numbers, what number is represented by the following matrix?
It is dual because p as defined here is 0 en.wikipedia.org/wiki/…
9h
comment In dual numbers, what number is represented by the following matrix?
If it were $\epsilon$, then subtracted by $\epsilon$ it would give 0. But it does not. Note that not only $\epsilon$ gives $0$ squared (for instance, $-\epsilon$).
9h
comment In dual numbers, what number is represented by the following matrix?
@Taladris its p-factor is 0 so it is clear dual.
10h
comment A question about fractional derivatives
Function 1-x or 1/(a-x)?
15h
comment Why does dividing by zero give us no answer whatsoever?
Why 0/0 should be 0, look here: math.stackexchange.com/a/1073101/2513
1d
comment Why these arguments for $\frac 00=0$ are not valid?
why it should be unique?
1d
comment Is $\frac 1 0$ undefined or equal to $\tilde{\infty}$?
It will if one defines 0/0=0 which is perfectly sane.
1d
comment Is $\frac 1 0$ undefined or equal to $\tilde{\infty}$?
The limit exists on the affine real line/complex plane.
1d
comment Is $\frac 1 0$ undefined or equal to $\tilde{\infty}$?
I want to answer this, please reopen.
1d
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?
1d
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.
1d
comment Why these arguments for $\frac 00=0$ are not valid?
@Lucian where I did?
1d
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.
1d
comment Why these arguments for $\frac 00=0$ are not valid?
@JiK it is equal, so?