What's your favorite polynomial?

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>>8636618
x^2 + 1 because it's the splitting polynomial for the complex numbers over R and it's extremely simply

it's also an example of a polynomial that's not zero as a polynomial but zero as a function when regarded over F_2

>>8636637
>zero as a function when regarded over F_2
0^2+1=0?

Whichever one that forms the bat symbol

>>8636618
1+x+x^2/2+x^3/6+...+x^n/n!
is an excellent polynomial.
It not only gets better as n goes to infinity, but the rate at which it gets better and the acceleration by which it gets better and so on are also proportional to n.

>>8636618
e^x obviously

>>8636783
>polynomial

>>8636667
:[

>>8636637
>>8636637
>it's also an example of a polynomial that's not zero as a polynomial but zero as a function when regarded over F_2
x^2+x works

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>>8636786
>implying

>>8636948
that's not a polynomial

>>8636637
Patrician choice

>>8636667
anon...

>>8636977
what?

>>8636948
polynomials have finitely many summands

>>8636948
I bet you also think e is a rational number because it's equal to a sum of infinitely many rational numbers.

>>8637016
But the space of polynomials has an arbitrary number of degrees so it has an infinite basis. So, in some sense it can be a polynomial.

>>8637121
>So, in some sense it can be a polynomial.
wrong

almost any major theorem about polynomials won't hold for the exponential

especially the most important ones like 'every non-constant polynomial has a root in the complex plane'

>>8637121
t. undergrad who doesn't know the difference between a direct sum and a direct product.

>>8637131
it has at -inf :^)

>>8637136
>in the complex plane

>>8637139
http://mathworld.wolfram.com/ExtendedComplexPlane.html

>>8636618
anything that isn't affine

>>8637140
like i said
>in the complex plane

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>>8637140
I understand that you're being intentionally disingenuous to get a rise out of people, but in the end you're only making yourself look like a tremendous brainlet.

>>8637143
The theorem also holds for the extende complex plane, its a weaker statement so no problems.
>>8637146
Maybe you are the brainlet anon, and cannot grasp my awesome ideas.

>>8637154
>Maybe you are the brainlet anon, and cannot grasp my awesome ideas.
You're just misusing well-known mathematical terms. I assumed you are baiting but maybe you are actually a moron. Terms like "polynomial" and "complex plane" have precise definitions, and making up your own definitions because you don't know the real ones is not "awesome" but rather a sign of ignorance.