Multiplication is a separate operation from repeated addition, but in definition. Peano arithmetic defines both multiplication and addition and they are indeed separate operations. However, if you look at where multiplication originated, it was first created as a result of repeated addition. Who ever came up with it probably thought, ‘look, I can repeatedly add numbers together! Oh no! how will I distinguish from 2(3) + 4 and 2(3 + 4), they must be separate operations!’

The arithmetic operations (not including the inverse operations) may be separate from each other but yield the iteration of the previous one while using natural numbers. That is why things like the up-arrow notation exist. We can’t rely on ideas like scaling for multiplication or growth for powers because we would run out of concepts when hyperoperations are brought up. I am certain Devlin would think pentation should not be taught as repeated tetration.

From a pedagogical point of view, teaching operations as repetitions of each other has worked up until now so I don’t see why it is an ‘outdated concept.’ And besides, Devlin seems so certain that he is right even though my guess is he probably learned using the ‘old method.’

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That being said, the post is meant purely to debunk things like these viral videos which misinterpret what the wage gap means. That video is incredibly misleading and made purely for political purposes based on no supporting data.

My rhetoric changes near the end where I call it “meaningless,” but you are right that it provides a rough idea that something might be going on and we should look into it more. I probably should have stuck to the “it doesn’t mean what people think” rather than the “meaningless” description.

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