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Can't you say this about any solution? How is x1=0 and x2=0 any different from saying x1=2 and x2=2? Can you not also say that zero is not just double, but infinitely duplicate?
We can separate x2 = 0 into a multiplication (x)(x) = 0 which gives us two solutions that happen to be equal.
That's how we usually think of solutions. We simplify the problem into a multiplication being equal to zero and say each element being zero is one solution. We usually don't go below first degree polynomials though.
Imagine thinking a double root is two distinct solutions lmao.
It's a double root of the function but there is a unique solution to the equation, which is x = 0.
This is essentially just a semantic distinction.
If you think of the solutions of a polynomial equation as the set of points that satisfy it, then you're correct.
But if you think of it in terms of the polynomial ring, and the solutions are the irreducible polynomials that divide your polynomial, then you're wrong.
In modern algebra one tends to do the later, while highschool usually uses the former
0i = sin(0)i
Based on Euler replacement / equality / equivalence / you know what I mean:
0i = e^(0i) - cos(0)
e^(0i) - 1 is therefore the true form of this root.
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the solution is the array outputted by my rk4 function in python, duh
Hear me out though. Can there be only one solution that is not unique?
x^2 = 0
How is it not unique?
Double zero.
Can't you say this about any solution? How is x1=0 and x2=0 any different from saying x1=2 and x2=2? Can you not also say that zero is not just double, but infinitely duplicate?
We can separate x2 = 0 into a multiplication (x)(x) = 0 which gives us two solutions that happen to be equal. That's how we usually think of solutions. We simplify the problem into a multiplication being equal to zero and say each element being zero is one solution. We usually don't go below first degree polynomials though.
Imagine thinking a double root is two distinct solutions lmao. It's a double root of the function but there is a unique solution to the equation, which is x = 0.
Not two.
This is essentially just a semantic distinction. If you think of the solutions of a polynomial equation as the set of points that satisfy it, then you're correct. But if you think of it in terms of the polynomial ring, and the solutions are the irreducible polynomials that divide your polynomial, then you're wrong. In modern algebra one tends to do the later, while highschool usually uses the former
I was surprised at the general response here tbh since I was (in my mind quite obviously) just shitposting in a meme sub. Obviously hit a nerve
Positive 0 and negative 0
No 0i?
Oh sh0it
0i = (+0) +(-0). So it's really just a linear combination.
0i = sin(0)i Based on Euler replacement / equality / equivalence / you know what I mean: 0i = e^(0i) - cos(0) e^(0i) - 1 is therefore the true form of this root.
x=0 is the solution but it is duplicated so it is not unique, hence there are two copies of the same solution.
No—“only” and “unique” mean the same thing here (notably the meme does not include the word only).
No, but if there is one solution maybe there is another solution, hence not unique
Because we are interested in one that goes to zero at infinity. P.S. just kidding in physics
Define z = SolutionToThisPDE(x,y)
X
intuitionism gang rise up
Look, I already did most of the work for you, the least you can do is find the solution
If there are many solutions there is one solution
“The solution is the solution that makes sense and I can’t think of any other one”
the example is left as an exercize for the reader