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

AI Thread Summary
The discussion revolves around proving the commutative property of multiplication for four or more factors. It highlights the challenge of constructing formal proofs, especially when geometric approaches seem inadequate for more than three factors. The commutative property states that the order of multiplication does not affect the product, exemplified by the equation abcd = dcba. A participant reflects on their initial confusion but acknowledges the validity of the property after further consideration. The conversation emphasizes the importance of understanding multiplication's fundamental properties, even when formal proofs are complex.
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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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