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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.

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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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