I think you mean physical dimensions. Mathematical dimensions work just like any other dimension (there’s nothing different about how the x dimension behaves compared to the y dimension).
Extra dimensions of space can be different. It’s possible that they’re just like the three physical dimensions we know and love. So you can move “forward” and *backward” along a new dimension just like the other three, and it sorta seems to extend to infinity, and is probably “flat” (if you walk in one direction, you will never return to where you started). So really the only different in this new dimension is that our brain can’t perceive it or even attempt to imagine it. But mathematically, x, y, z, and new dimension are interchangeable. Same rules.
But it’s possible the new dimensions are different. In one version they’re “compactified.” Instead of extending into infinity and being basically flat, they may be circular and quite small. As you move along the new dimension in one direction, you eventually return to where you started. But theyre so small that only quantum sized objects really interact with them (e.g., they’re like the size of a single electron or something). So to big things like us and a baseball, these tiny dimensions may as well as not exist. But they solve some physics problems.
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