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They might be describing something equivalent to it. That doesn't mean they're describing it. Funny thing about mathematics: every single way of describing or talking about any mathematical phenomenon is mathematically equivalent, or wrong.


Doesn't this just come down to whether you consider there to be any philosophical difference between isomorphism and equality?


There's a difference? Heathen!


I consider isomorphism to be isomorphic to equality. Interpret that as you wish.


Huh, that's an interesting thing to think about, and considering that I probably would've worded my comment differently. Thanks.




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