Why topological invariants instead of topological invariances?

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SUMMARY

The discussion clarifies the distinction between the terms "invariant" and "invariance" in the context of mathematical terminology. "Invariant" serves as both an adjective and a noun, indicating an object possessing the property of being invariant. In contrast, "invariance" is strictly a noun that describes the property itself. This nuanced understanding highlights the complexity of language, particularly in mathematical discourse.

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Isnt it invariant an adjective?
 
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Because that's the way English is.

"Invariant" is indeed an adjective, but it is also a noun referring to something that has the property of being invariant. In the (tautological) sentence "I know that this quantity is an invariant because it is invariant", the word "invariant" is used twice, once a noun and once as adjective.

And "invariance" is also noun, but it refers to the property that is described by the adjective, not to an object that has that property: "I know that this quantity is an invariant because is invariant, which is to say that it has the property of invariance".

English is weird. I love it for its quirkiness and expressive power, but it's still weird.
 

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