In theory, a two-dimensional sword that is infinitely thin would have no thickness, meaning it would have no resistance or obstacles to cutting through objects. However, it's important to note that such a sword is purely a concept and does not exist in reality.
In our three-dimensional world, objects have thickness and physical properties that determine their resistance to being cut. Even the sharpest real-world sword has limitations based on its material and the properties of the object being cut. Additionally, cutting through certain materials may require more than just sharpness, such as applying sufficient force or using appropriate techniques.
So while a two-dimensional sword without thickness might be a fascinating concept, it's not something that can be applied practically in our physical reality.