Yes, division is a cool idea. One place you see a lot of it is "Ah my Goddess" - Urd does it, and Belldandy does sometimes.
Another story idea is a spell that says it lets you be in two places at once. Then you cast it and - oops! there are two half sized versions of you! Even if the two of you are truly identical, you might eventually end up not trusting that the other you is really you.
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