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2d
comment Showing that $7+\sqrt[3]{2}$ is an algebraic number
Ive always wanted to really put the effort in showing the intuition-behind-the-intuition. I am very glad you took the time to go that second level step of why we ought to even shift things over in the first place. Often its the motivation behind that motivation, such as here, that many don't know how to connect
2d
comment Solution to following functional equation
@wythagoras yea now that I think about that is a better formulation of what I wanted to ask
2d
asked Solution to following functional equation
May
25
awarded  Civic Duty
May
24
comment Calculate the sum of three series which may be telescoping
See @Tim Raczkowski's hint for the third one
May
24
answered Calculate the sum of three series which may be telescoping
May
2
accepted Zeroes of sin(x)
May
1
comment Zeroes of sin(x)
So this shows that all solutions MUST lie on the real line but it doesn't tell me that there CANNOT be solutions that aren't an Integer multiple of $\pi$. I guess concretely what I mean to ask is, how can i be guaranteed that there isn't a real number x such that $x \ne k \pi $ for any $k \in \Bbb{Z}$ yet $\sin(x) = 0$
May
1
comment Zeroes of sin(x)
How do we know that these are the only values. As in how can I be sure that there is there no value $y$ such that $y$ is NOT an integer multiple of $\pi$ and $e^{y} = 1$ or $e^{y} = -1$? Thats the crux of my issue
Apr
29
asked Zeroes of sin(x)
Apr
11
asked Is every natural recursive relation necessarily holomorphic?
Mar
28
asked Q Pochammer Symbol Product Identities
Mar
28
comment Infinite sum involving ascending powers
I have question, The sum that I gave above definitely converges for all x, if $a > 1$ and $a \in \Bbb{R}$ yet the expression you gave doesn't converge unless $|a|<1$ That suggests to me an analytic continuation is necessary. What is the analytic continuation I'm looking for?
Mar
21
accepted Artificial Integer?
Mar
21
comment Artificial Integer?
@ThomasAndrews Yep! I think you had the exact same line of thought back then as I am beginning to explore onw
Mar
21
comment Artificial Integer?
I wanted it to be as general as possible while still being consistent with the laws of modular arithmetic. In other words if $a \equiv b \mod N$ then $f(a) \equiv f(b) \mod N$ do there exist non polynomial functions that satisfy that?
Mar
21
comment Artificial Integer?
In the even the function is defined cleanly ${\Bbb{Z}}/{\Bbb{N}}$ does that change things significantly?
Mar
21
comment Artificial Integer?
How to reconcile these two? @Thomas Andrews
Mar
21
comment Artificial Integer?
See my comment underneath @ThomasAndrews for the tricky part with |x|
Mar
21
comment Artificial Integer?
I still have issues with the answer though, namely that $|x|$ isn't well behaved. I don't think this is the question I really mean to ask, but I'm trying to figure what question I should be asking. There needs to be restriction on f in this case