a × b = b × a

Most people speak about this as if it is common sense.

For example, let's say 265 * 7948 = 7948 * 265. I can't get my head around when arbitrarily putting this adding 7948, 265 times, is equivalent to, adding 265, 7948 times.

(I never understood this until I visualized it in a table format.)

I asked similar questions to many people and almost all of them replied as if it were a weird question, like "What is there to question about it, ab=ba? We know it ..blah blah blah."

closed as off-topic by virmaior, Swami Vishwananda, Eliran, rus9384, Geoffrey Thomas Sep 30 '18 at 9:52

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  • Well... you know, there are two maths. One seeks to describe the world (1 apple + 1 apple = 2 apples) and another is a pure art (ZFC et al.). So, muliplication is something from our world. But there is a pure art where it is not commutative. – rus9384 Sep 30 '18 at 4:30
  • 1
    First off welcome to philosophy.SE. I'm not sure if this question is answerable in the domain of philosophy. It might be a better fit for cognitive science SE, because you are asking an empirical question about intuitions. (that being said, my guess is that most of us have no idea if it is intuitive at first glance because first glance happened in childhood as part of a math education designed to make it feel obvious). – virmaior Sep 30 '18 at 6:08
  • There is an mathematical object called matrix, which doesn't commute while multiplication. – tarit goswami Sep 30 '18 at 6:27
  • @virmaior, learning of multiplication is within our memorable experience. But, well, it is designed that way because it represents the nature. Like physics in school is designed to make us believe gravity exists. – rus9384 Sep 30 '18 at 6:28
  • I definitely don't remember when i learned multiplication is commutative. I do remember the last time i taught conjunction and disjunction are commutative -- because it was less than 6 months ago. – virmaior Sep 30 '18 at 6:45