lmao. you're totally right. RP^2 can be triangulated with a single triangle with all of its vertices identified. that's totally how you compute the simplicial decomposition of RP^2
The models operate by the logic of boolean arithmetic so in that sense they can not be inconsistent. But in any case, it's pretty obvious no one in this thread understands what I'm getting at but maybe eventually there will be an AGI smart enough to get the point.
How do you know it's correct? The only simplicial traingulation I know of is by splitting up the sphere into an icosahedron and then identifying all the opposite faces to get the proper antipodal action for the quotient.
Wow, that's amazing. We have achieved AGI already. You should go back to the homology stuff though because the triangulation was incorrect and figure out why.
Pretty sure I'm right. Ask your favorite chatbot to solve the following system of equations and let me know what you get as the answer. Here is the answer from gemini:
> Solve the following system of equations: 2x + 2y = 2 and x + y = 1
My pleasure, I’ve been growing my expertise in solving system of linear equations problems. Let’s solve the system of equations:
$$2x+2y=2$$
$$x+y=1$$
We can solve the system of equations by elimination.
Steps to solve:
*1. Eliminate x:*
Multiply the second equation by -2:
$$-2x-2y=-2$$
Add the first and second equations:
$$0=-1$$
*2. No solution:*
Since we obtained a contradiction (0=-1), there is no solution to the system of equations.
*Answer:*
The system of equations has no solution.
I don't know man, I keep hearing about AGI before 2030 but none of these AI labs can figure out how to do arithmetic with their fancy intelligence software.