If we consider a hypothetical 2-dimensional sword that is infinitely thin, it would still face limitations when trying to cut through objects in our three-dimensional world. While the sword may be infinitely sharp along its edge, it would lack the necessary thickness and structural integrity to exert significant force or resist resistance.
Cutting through objects requires both sharpness and force. The sharpness of the sword's edge would allow it to penetrate a material up to a certain point. However, the lack of thickness would prevent it from exerting enough force to continue cutting or to overcome the resistance of the material being cut.
Additionally, real-world objects have depth and are composed of atoms and molecules arranged in three dimensions. A 2-dimensional sword would struggle to interact with objects in this manner. It would be unable to slice through three-dimensional structures like bones, thick branches, or dense materials.
In summary, even if you had an infinitely thin, 2-dimensional sword, it would face limitations in cutting through objects in our three-dimensional world due to the lack of necessary force, thickness, and structural integrity.