What's your favorite polynomial?

what is your favorite #1 biggest polynomial

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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

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

Whichever one that forms the bat symbol

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.

e^x obviously

>polynomial

:[

>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

>implying

that's not a polynomial

Patrician choice

user...

what?

polynomials have finitely many summands

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

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.

>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'

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

it has at -inf :^)

>in the complex plane

mathworld.wolfram.com/ExtendedComplexPlane.html

anything that isn't affine

like i said
>in the complex plane

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.

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

>Maybe you are the brainlet user, 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.