ELI5: In music, why can’t I switch the order of notes in an inversion?

r/

Let’s take a major triad like CEG, you can do 2 inversions: EGC and GCE, but not something like GEC, as that wouldn’t be considered an inversion of the C major triad.

But why? It’s the same notes arranged differently. I’ve tried to figure out what GEC would be called then if it’s not C major 2nd inversion as the root note would be G and it contains all 3 notes from a C major chord, but apparently this is not correct?

Can someone please help me understand this.

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