Playing a chord rooted with any chord degree except the root on the bass string.

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I need help understanding the concept of chord inversions.

This article from wikipedia, states: In the first inversion of a C major triad the bass is E—the 3rd of the triad—with the 5th and the root stacked above it (the root now shifted an octave ...
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Sixth and Minor Seventh inversions conflicts

For example consider C6 [C-E-G-A] and Am7 [A-C-E-G] which share the same notes in different order. When we play [E-G-A-C] how is it called?(is this a inversion of C6 or Am7) Generally, how are these ...