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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.
Dec
17
comment Explanation of method for showing that 0 / 0 is undefined
The second equality is only true if $$x\ne(-x)$$ Zero does not satisfy this, so only the first one is correct.
Dec
9
comment Series diverging to infinity and series converging to infinity - is there a difference?
@rank no. Sequence of 1+1+1+1+... diverges to infinity. But can be summed up to -1/2. I wonder whether there are separate series about which one can say that they converge to infinity.
Dec
9
comment Why we cannot ascribe values to behavior of functions at poles?
Good point. I will think about it.
Dec
9
comment Convergence of Newton series
@Jack M since he is speaking about forward difference, it can be assumed the points are equidistant, 1-separated unless one mentions time scales.
Dec
8
comment Why we cannot ascribe values to behavior of functions at poles?
@AlexR yes, this Caushy principal value is the real part of what I propose as a value of a function in a pole point. The other part is the same, but with another sign: $$\lim_{h\to 0}\frac{f(x+h)-f(x-h)}2$$ It will not be a real number (if the function has a pole in $x$, otherwise of the function is continuous it will be zero) but can be expressed in terms of $\omega$.
Dec
8
comment Zeta and Gamma function regularization with $\omega=1/0$
@Lucian for Zeta also.
Dec
8
comment Zeta and Gamma function regularization with $\omega=1/0$
@Antonio Vargas there was a typo in the formula, sorry (actually I inserted the wrong formula).