No solution for $x$.

If you want a answer that isn't that, $\begin{aligned}\ |&x|<0 \\ &\uparrow \\ \text{Right}&\text{here} \end{aligned}$

To everyone coming up with complex numbers:

For a complex number of the form $a+bi$, we have that $|a+bi|=\sqrt{a^2+b^2}$.

Therefore we have that $|i|=|0+1*i|=\sqrt{0^2+1^2}=\sqrt(1)=1$

Also, $i^2=-1$, so $|i^2|=|-1|=1$

If something is less than $0,$ then it is also less than every number greater than $0.$ Thus, if $|x|<0,$ then $|x|<3.$ This shows that the person loves the absolute value function because <3 is a heart. All we need to do is prove that someone loves the absolute value function. I love the absolute value function, so it is indeed possible. $\mathbb{Q.E.D.}$

for me this is peculiar since the other day i had a thought about a number with a smaller magnitude than 0 and thought i'd stumbled upon some new realm of mathematics lol. this is my best attempt at it, though im pretty sure its fraught with logical errors i thought i'd give it a try xD |x|<0 ---> |x|=-k (k is a positive real number) ---> e^|x|=e^-k ---> e^(|x|+k)=1 ---> |x|+k=(2πn)i ---> |x|=-k+(2πn)i ---> x=inverseabs(-k+(2πn)i) ---> |A+Bi|=-k+(2πn)i =sqrt(A^2+B^2) ---> A^2+B^2=k^2-4πkni-(4(π^2)(n^2)) ---> B=sqrt(k^2-4πkni-4(nπ)^2-A^2) --->

x=A+sqrt(k^2-4πkni-4(nπ)^2-A^2)i

there is no way thats right lol

Here's a solution set where $|x|<0$ for any $x\in\mathbb{O}$ (Octonion):

$\Huge \{\}$

DNE

Only solution might be when x represents a matrix but in that case it would represent a determinant symbol

There is no solution.Or if this is a math joke,$x$ is between the vertical lines.

It's not $i$ since the norm of it is 1.

What is very much possible is to have $x$ be a matrix with a negative determinant, thus the condition holds. But apart from that, norms are defined to be nonnegative on inner product spaces, so this only happens on very specific cases.

Since I've been absent for 2 weeks, you get 2 hints.

its been so long and i don't think anybody is close to answering this, could you just explain what it is?

it's been too long and as nobody has solved this i highly doubt it has an established answer among the maths community, i would like to hear what the solution to this is, would be very educational i presume

To all of you saying "DNE", you are wrong (as the title says). Here are the hints to guide you out: 1. Do not try to solve this problem using traditional mathematics. 2. Think outside of the realm that lies outside the box (i.e outside of outside the box). 3. The solution is yet as close to infinity as it is far away from it. For each of the seven days that there is no right solution, I'll put up an additional hint.

The correct answer is i^2. Since i=square root of -1, then i^2 = -1. => imaginary numbers

x = i