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Dec
21
comment No difference between $0/0$ and $0^0$?
@njguliyev $0\cdot \infty$ is usually counted as 0 (in cardinal and ordinal arithmetic, in Lebesque integration etc). 0/0 is better defined as 0 (see here math.stackexchange.com/questions/527613/…) and if $0^0=1$ then its logarithm is also 0. So all fits well.
Dec
18
comment Why Not Define $0/0$ To Be $0$?
you "proved" by multiplying all by $0$. $0$ is a number.
Dec
18
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.
Dec
18
comment In dual numbers, what number is represented by the following matrix?
what reasoning do you mean?
Dec
18
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)
Dec
18
comment In dual numbers, what number is represented by the following matrix?
the last matrix is $-i$.
Dec
18
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 $i+\epsilon$?
Dec
18
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/…
Dec
18
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, $-\epsilon$).
Dec
18
comment In dual numbers, what number is represented by the following matrix?
@Taladris its p-factor is 0 so it is clear dual.
Dec
18
comment A question about fractional derivatives
Function 1-x or 1/(a-x)?
Dec
18
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
Dec
17
comment Is $\frac 1 0$ undefined or equal to $\tilde{\infty}$?
It will if one defines 0/0=0 which is perfectly sane.
Dec
17
comment Is $\frac 1 0$ undefined or equal to $\tilde{\infty}$?
The limit exists on the affine real line/complex plane.
Dec
17
comment Is $\frac 1 0$ undefined or equal to $\tilde{\infty}$?
I want to answer this, please reopen.
Dec
17
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?
Dec
17
comment Explanation of method for showing that 0 / 0 is undefined
So u claim $0\ne -0$ based on analogy with other numbers? See here: math.stackexchange.com/questions/1071821/…
Dec
17
comment Explanation of method for showing that 0 / 0 is undefined
@5xum the first one follows from the algebraic properties of 0, the second one follows from the property $x\ne-x$. We know that $x\ne-x$ for all real numbers except 0, but this does not mean the same should be preserved in 0.
Dec
17
comment Explanation of method for showing that 0 / 0 is undefined
@5xum in that set 1 has different properties than in real numbers. In real numbers, if x/x =1(real), then $x\ne-x$, because $1\ne-1$. If in a set 1=-1, then this condition does not apply.
Dec
17
comment Explanation of method for showing that 0 / 0 is undefined
@5xum because $x/-x=-1$. Thus since $0/0=0/(-0)$, the solution of $x=0/0$ should satisfy $x=-x$. It can be only either unsigned infinity or 0.