> The problem lies that it is hard to imagine something that does have zero dimensions.
Do you really think so? It’s not hard to picture the real number line, with the point zero (or any other single point) distinguished. Sure — if you draw it in the standard schematic way you have to give it some area, but it still seems quite intuitive that it’s ‘zero-dimensional’. Especially if you play around with converging sequences and open sets and stuff; you quickly develop intuition for what it means to be a point rather than something higher dimensional.
Do you really think so? It’s not hard to picture the real number line, with the point zero (or any other single point) distinguished. Sure — if you draw it in the standard schematic way you have to give it some area, but it still seems quite intuitive that it’s ‘zero-dimensional’. Especially if you play around with converging sequences and open sets and stuff; you quickly develop intuition for what it means to be a point rather than something higher dimensional.