>taking signal processing course to see how much of a joke

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>taking calculus class
>professor says "let x be a real number"

>>8596202
Dirac delta function is named dirac delta function even if it's not really a function.
>>8596205
Totally sensible thing to say.

Am I falling for a bait dammit.

>>8596202
if it was good enough for Paul Dirac,
then it's good enough for you fgt pls

>>8596224
>Totally sensible thing to say.

Totally retarded thing to say in a calculus class.

In a calculus class professors never tend to explain the logical significance of real numbers. Sure, when they define continuity they talk about intervals of real numbers and functions defined on the real numbers but a student knows fuck all about why the real numbers are important.

A calculus student could perfectly think that a rational function could be continuous, as limits can be defined for rational functions. Limits can even be defined for natural numbers, but there it is a little more obvious that natural functions are obviously discontinuous.

And is that is the case, then what is even the point of reminding the student that x is a real number. The student does not understand the significance of real numbers for calculus, which is why in mathexchange there are a bunch of questions asking "Why can't we do calculus in the rational numbers".

>lecturer claims every polynomial has a root
>put my hand up, say what about x^2+1=0
>lecturer is visibly embarrased

>>8596404
plus or minus i

>>8596404
He will probably just make up some numbers that are defined to be the answer.

>>8596409
>Just defining a new number to make up an answer

Okay, two can play that game. Let i(x) be the super imaginary polynomial that has no root at all.

>>8596400
>in 1st grade
>teacher asks us to add the numbers 3 and 5
>she hasn't even introduced the set theoretic definition of the naturals
>triggered
>raise my hand and tell the teacher we should learn the fundamentals first
>sent to the principal's office for being 23 years old and in a first grade classroom

>>8596413
You mean like i(x) = 2i?

Was this supposed to be a trick?

>>8596436
>i(x) = 2i

That is not a polynomial

But, just as "mathematicians" don't have to show us how i looks, I also don't have to tell you how i(x) looks

i(x) is simply the polynomial that has no root. It is defined that way.

I can do that, just like you define i to be the root of -1. If you can play that game of "the answer is what is the defined as the answer" then I can do the same.

>>8596441

> Defining something that doesn't exist

Anything you'll ever prove about i(x) will be a vacuous truth. Also

> just as "mathematicians" don't have to show us how i looks

you can simply admit you know nothing. It's okay to not know.

A number can't not be real unless it's a letter that's not in the integrel sign, like if I say integrel of xdx then obviously x is real but if I said 'i' or something, wouldn't be part of the real numbers in there.

>>8596441
I know you think you're smart after watching some Berger lectures, but 2i is indeed a polynomial. It's just constant. And it has no roots.

And in math, when you say let "let A be the objects such that ..." you are required to show that such an A exists. It doesn't have to be a constructive proof, but you still have to do it.

Take more math classes before you try to have another opinion on math.

>>8596458
>but 2i is indeed a polynomial

Oh, if that is how you define polynomials then that is great me!

Then i(x) = 1

That has no root. Nice contradiction of the FTA. Too easy.

> you are required to show that such an A exists.

No, you can also define things. When you say "let i be the square root of -1" you cannot prove that it exists. You have to define it as a separate object.

>>8596464
Reread the FTA you fucking idiot.

>>8596466
>Reread the FTA you fucking idiot.

No, you reread you absolute autist. When I was talking about i(x) I obviously meant in the context of polynomials that qualify for the FTA.

I am simply saying that let i(x) be the polynomial without root.

Now, maybe this polynomial is a complex polynomial. Not a complex-variable polynomial. But a complex polynomial. The complex polynomials being a made up set I made up right now that includes all real polynomials and i(x)

>people do not sage and report old pasta bait threads

Shameful.

>>8596469
>When I was talking about i(x) I obviously meant in the context of polynomials that qualify for the FTA.
Then why did you say "2i is a not a polynomial" when you should've said "2i is not a polynomial which the FTA applies to"? You're just trying to save face by lying now. There is not shame in admitting you were wrong.

>I am simply saying that let i(x) be the polynomial without root.

Then i(x) is a constant polynomial (by the FTA). You cannot define i(x) to be a non-constant polynomials with no complex roots because we know that no such objects exist. In a similar way, you can't say "let i be the real solution to f(x) = x^2 +1" because no such x exists. You can construct new objects, like i, but not if they contradict what is already known.

Look man, you need to learn some fucking terminology before you try this shit again.

2i and all other complex constants are indeed polynomials. They are constant polynomials.

We don't call things "variable polynomials" we call them "non-constant" polynomials.

Complex polynomials is a set which already exists.

>>8596490
>You cannot define i(x) to be a non-constant polynomials with no complex roots because we know that no such objects exist.

I know no such object exist, which is why I am defining it, just like i is typically defined.

You are simply being ridiculously autistic about wording when you knew what I was saying. You are in a fucking forum for fucks sake. Chill the fuck down.

i(x) is the non-constant polynomial with no root. Happy?

>>8596496
nigga u gay

>>8596496
That's akin to saying let A and not A. Anything follows from a contradiction my man. Your new polynomial is useless, just like every single one of Berger's lectures.

>>8596202
https://en.wikipedia.org/wiki/Spede_Pasanen

>>8596413
>>8596441
This guy gets it. I stopped caring about math when I was introduced to the concept of imaginary numbers. What a crock of shit. If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for algebra solutions that basically say "the correct answer is whatever the correct answer is". Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

Math is logical and numbers never lie my ass. Math is just as flawed as any other human construct.

>>8596677
>Only my invented shit is true shit
Your point can be applied for every axiom, yet we do not discard summing things for that reason.

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>>8596202
>>8596648
Forcing a meme is real

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>>8596705
It's not a forced may may but it's old and is pretty much ded.

Also what's the best book for DSP?

>>8596400
>chem 101 class
>prof starts talking about basic atomic structure
>doesn't even mention the word eigenfunction
>homework contains no differential equations or linear algebra
I know exactly how you feel

>>8596677
You can't argue against the usefulness of complex numbers.

Don't lie, you didn't stop caring about math when you started diagreeeing with the foundations of math. You stopped because it got too hard for you.

Goddamn brainlets always blaming others for their problems.

>>8596432
kek

>>8596909
> arguing with copypasta in a troll thread
lurk moar newfag

>>8596496
I think they are too autistic to get the joke.

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Alright, you faggots. If you believe in that "imaginary" number i. Can you tell me what does i look like in decimals? Every number has a decimal expansion. So what's the value of i?

>>8596677
Then how is math using complex numbers so incredibly predictive of things?

You're just slow mate.

>>8597537
Complex numbers are defined that way

>>8597484
Who said every number has a decimal expansion?

>>8596496
There is a clear definition of what a polynomial is. Given our standard axioms, it is possible to prove that every non-constant polynomial has at least one complex root. Therefore, the introduction of your axiom "there exists a non-constant polynomial with no roots" give rise to an inconsistent system, where a statement P can be both true and false at the same time.

The definition of i does not have that problem.

>>8596413
>Just defining a new number to make up an answer
Same was done with reals, to give answers to problems that had no answer in rationals, rationals were made up to solve problems that had no answer in integers, negative integers were made up to solve problems that had no solution in naturals, even the naturals were made up, contrary to Kronecker's claim

>>8596496
But you know saying "define...", "let...", "... is ..." doesn't make your claim true, right?

>>8596677
>inventing numbers that can't exist
Prove me 3 exists

>the correct answer is whatever the correct answer is
Yes, and it works because emprically universe is consistent

Hilarious OP xD never seen this thread before

>>8597484
i.0

>>8596677
How do people still fall for this?

>>8596441
It is a polynomial. If f(x)=0, it'd be a constant zero polynomial (with an undefined degree), if f(x)=1, it'd be a constant polynomial with degree 0, f(x)=2x, it'd be a linear polynomial with degree 1.

FTA only cares about nonconstant polynomials, so f(x)=2x still counts, however, FTA just states it has a complex zero (also called a root), which it does, so f(x)=2x isn't a counterexample.

>>8596458
>2i =/= 0 for all i in C
2x=0, solve for x. "root" means the same thing as zero.

>>8596464
>>8596469
It has to be nonconstant. Did you really think disproving a major well known theorem that is the foundation of almost all the math we do would be as easy as "lol i(x)=1 what now nerd?"

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>>8596202
dam...u gotta look like this to understand this thread

>>8596432
i lel'd

>same thread with the same replies and the same pasta

Ever feel like you're dead but nobody told you?

>>8600206
actually i phrased the OP slightly differently than normal

>>8600206
Don't forget, you're here forever.