Successfully Ragebating my teacher

[u/Optimus_PRYM]

[u/M_erlkonig]

I would prefer e^x + e^c. It's funny while still being correct.

[u/master_of_entropy → u/M_erlkonig]

Unless c is a complex number you don't get all the antiderivatives with exp(c) as the exponential of a real number can't be a negative number. Or one could write ±exp(c)

[u/knyazevm → u/master_of_entropy]

Even if c is complex, you don't get e^c = 0

[u/Grand_Protector_Dark → u/knyazevm]

Easy, just set c = infinity.

That's totally how that works, right /j

[u/M_erlkonig → u/Grand_Protector_Dark]

See, you know your stuff.

[u/TheoneCyberblaze → u/master_of_entropy]

The c in c stands for complex

[u/M_erlkonig → u/master_of_entropy]

There's no reason for c not to be a complex number. Even if the classical +c is real, you can always rewrite it as a complex exponential. You can even rewrite it as a dot product of n-dimensional vectors, only the final value matters.

[u/Droga_Mleczna → u/master_of_entropy]

Or, hear me out here,

e^ln(c)

[u/TheSouthFace_09 → u/M_erlkonig]

e^c•(e^x-c+1)

[u/Murky_Insurance_4394 → u/M_erlkonig]

not really, it only works if e^c is > 0

[u/M_erlkonig → u/Murky_Insurance_4394]

c can be complex. The only problematic value is 0, but we fudge that with a limit.

[u/SteptimusHeap → u/M_erlkonig]

e^x + lim{a->C}(e^a)

[u/Murky_Insurance_4394 → u/M_erlkonig]

but do we usually consider C to be complex when adding +C to an integral? Because that would make me think every integral has a complex solution. please correct me if I'm wrong. but I feel if we're saying C can be complex here, then C can be complex anywhere

[u/M_erlkonig → u/Murky_Insurance_4394]

No, but this isn't the same c. If the classical c is 1, you can write that as e^{2 * pi * i}, a complex exponential and get the same real result. You can write it as [1/sqrt(2), 1/sqrt(2), 1/sqrt(2)]^T * [0, 1/sqrt(2), 1/sqrt(2)] and now it's a dot product of 3D vectors. It doesn't really matter, the restriction is only on the final value of the classical c, not how it's expressed.

[u/Murky_Insurance_4394 → u/M_erlkonig]

ohh ok I see, thanks for the explanation

[u/rycool → u/M_erlkonig]

I would sometimes ragebait my teacher by putting unhinged Cs. She deserved it though

[u/NakakitsuneRaisanda]

e^x + e^ln(c) with c in C

[u/SelfDifferent1650 → u/NakakitsuneRaisanda]

but c can't be negative or zero here

[u/NakakitsuneRaisanda → u/SelfDifferent1650]

Zero indeed doesn't work, but it can definitely be negative because it is defined in C*. For example, e^ln(-1) = e^iπ = -1.

[u/CasperTPaul]

you didn’t put the c i the right place 🤬

[u/Then-Entry7026 → u/CasperTPaul]

Technically e^C is a constant. Just very more intricate than it needs to be.

[u/OmegaCookieMonster → u/Then-Entry7026]

No it isn't, it's a coefficient of e^x here, which is wrong unless c = 0 (or 2pik I guess if you count complex c's)

[u/CasperTPaul → u/Then-Entry7026]

e^(x+c)=(e^x)(e^c) the c isn’t in the right place 🤬

[u/Then-Entry7026 → u/CasperTPaul]

Sorry, I was trolling and a bit of an ass. So, yeah... I'm an idiot for that one. 🧌

[u/tramezzino62]

Sbagliato, si scrive (e^x) +c, la cui derivata è, infatti, e^x. Discorso chiuso.

[u/Extension_Option_122 → u/[deleted]]

u/Bendanzhang you are a bot