How do you prove the commutative property of multiplication for 4+ factors?

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The discussion focuses on proving the commutative property of multiplication for four or more factors, specifically demonstrating that abcd = dcba. The commutative property states that the order of multiplication does not affect the product, as illustrated by the equation abcd = (ba)(dc) = (dc)(ba). The conversation highlights the challenge of visualizing this property geometrically for more than three factors, emphasizing the algebraic approach instead.

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hamsa0
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I don't know how to construct formal proofs but there is the obvious geometric approach for 2 and 3 factors. However, how do you prove the commutative property holds up for 4+ factors? You end up with a lot of different orders in which you can multiply the factors and you can't just construct a geometric object from them.
 
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I don't see where geometry comes into it.
The commutative property of multiplication says that ab = ba. For 3 factors it would be abc = cba. For four factors, I guess you're trying to prove that abcd = dcba.
abcd = (ba)(dc) = (dc)(ba) = dcba
 
Ya after I posted this and hopped on the bus I realized it was a retarded question lol. Thanks for the response though man.
 

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