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Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
26
comment Is there a formula to quickly express delayed functions in terms of finite differences?
@Did what is inflammatory in unaccepting a wrong answer and accepting a correct one?
Jun
25
comment Is there a formula to quickly express delayed functions in terms of finite differences?
Thanks for the correction, but copying my answer and downvoting it is not a good behavior.
Jun
25
comment Is there a formula to quickly express delayed functions in terms of finite differences?
Can anyone explain the downvote?
Jun
25
accepted Is there a formula to quickly express delayed functions in terms of finite differences?
Jun
25
answered Is there a formula to quickly express delayed functions in terms of finite differences?
Jun
25
comment Is there a formula to quickly express delayed functions in terms of finite differences?
This is wrong, $y(x+2)=\Delta^2 y(x)+2\Delta y(x) +y(x)$ Where is the coefficient in your formula?
Jun
15
comment If two functions are equal to their Newton series, is their composition also equal to its Newton series?
@Giuseppe Negro well, I has been given a counter-example: $f(x)=\sin(\pi \sqrt{x})$, $g(x)=x^2$
Jun
15
revised Were there attempts to build a system of numbers where division by a negative number is greater than division by any positive number?
added 27 characters in body
Jun
15
revised Were there attempts to build a system of numbers where division by a negative number is greater than division by any positive number?
added 168 characters in body
Jun
15
comment Were there attempts to build a system of numbers where division by a negative number is greater than division by any positive number?
well I've read that article. It says "A substance with a negative temperature is not colder than absolute zero, but rather it is hotter than infinite temperature." This means that even though it has some properties of negative temperature, its energy level is still greater than that of cold quantities. As such, the sustem with "higher than infinite" temperature can be distinguished by measuring the total energy. This creates well-ordering. So it is exactly what I am talking about: not a circular real line, but a spiral one.
Jun
15
comment Were there attempts to build a system of numbers where division by a negative number is greater than division by any positive number?
I want the tangent of 3/4 pi be greater than the tangent of 1/4 pi. That is the tangent to be monotonously increasing. This is applicable in geometry and in physics when measuring speed of particles. On projective real line they are equal (just as on non-extended real line).
Jun
15
comment Were there attempts to build a system of numbers where division by a negative number is greater than division by any positive number?
The projective real numbers line is not ordered, so the whole point of this quention is ignored.
Jun
15
asked Were there attempts to build a system of numbers where division by a negative number is greater than division by any positive number?
Jun
15
comment If two functions are equal to their Newton series, is their composition also equal to its Newton series?
@Giuseppe Negro there is no total analogy though. If we allow complex functions, then there is a counter-example, for instance, $g(x)=2\pi i x$, $f(x)=\exp(x)$. That's why I limited the question to real-valued functions.
Jun
15
comment Modified division, hyperreal numbers and transfinite derivatives
No, $\frac{a}{-b}\ne\frac{-a}{b}$
Jun
15
revised Modified division, hyperreal numbers and transfinite derivatives
added 141 characters in body
Jun
15
asked Modified division, hyperreal numbers and transfinite derivatives
Jun
14
accepted Can any analytic function be represented as a sum of a Newton series and a periodic function?