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Jan
24
revised Need an operator with given properties
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Jan
24
revised Need an operator with given properties
added 16 characters in body
Jan
24
comment Need an operator with given properties
@Cameron Williams as $+\infty$
Jan
24
comment Need an operator with given properties
@Cameron Williams zero to $x$ power.
Jan
24
comment Need an operator with given properties
@Cameron Williams the class is any functions defined in the neighbourhood of zero (not necessarily in zero itself), icluding values from affinely extended real line.
Jan
24
revised Need an operator with given properties
added 29 characters in body
Jan
24
revised Need an operator with given properties
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Jan
24
revised Need an operator with given properties
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Jan
24
comment Need an operator with given properties
@Cameron Williams I need an operator that works primarily on analytic functions, but also desirably on functions of more generalized classes, including non-continuous in zero and distributions.
Jan
24
revised Need an operator with given properties
added 83 characters in body
Jan
24
asked Need an operator with given properties
Jan
24
comment Differentiable only at $x=0$ and $f'(0)>0$
The example of David Mitra satisfies the first two conditions.
Jan
24
comment Differentiable only at $x=0$ and $f'(0)>0$
@user197137 the definition of derivative is $\lim_{h\to 0}\frac{f(x+h)-f(x)}h$. If it is positive, then there are infinitely many such h that $f(-h) < f(0)< f(h)$
Jan
24
comment Differentiable only at $x=0$ and $f'(0)>0$
@user197137 for the function to have positive derivative, such h should exist.
Jan
24
revised Using the rules that prove the sum of all natural numbers is $-\frac{1}{12}$, how can you prove that the harmonic series diverges?
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Jan
24
answered Using the rules that prove the sum of all natural numbers is $-\frac{1}{12}$, how can you prove that the harmonic series diverges?
Jan
24
comment Numerical system that includes the limit targets such as $0^+$, $0^-$, $1^+$ etc
@ajotatxe limit will be excessive in this case, in this numerical system the function can be evaluated directly: $\sin 0^+=0^+$. You can see it as the simplifyed system of hyperreals, with $0^+$ substituted for any positive infinitesmal.
Jan
24
revised Numerical system that includes the limit targets such as $0^+$, $0^-$, $1^+$ etc
added 46 characters in body
Jan
24
asked Numerical system that includes the limit targets such as $0^+$, $0^-$, $1^+$ etc
Jan
24
answered Could “$\infty$” be understood by taking the reciprocals of the Hyperreal numbers?