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by Swiffy0 786 days ago
Isn't the whole point of the term "invariant" that it describes something as unchanging under specific circumstances.

e.g.

The sum of the angles of triangles is 180 degrees in the context of euclidean geometry. However, if we project a triangle on a sphere, this no longer holds. So the sum of the angles is an invariant under euclidean geometry.

On the other hand, the value of PI is a constant because it stays the same regardless of the circumstances. That's why all the numbers themselves are constant as well - the number 5 is number 5 absolutely always.

So if you have a value that changes over time, it is definitely not a constant. It could be invariant, if you, e.g. specify that the value does not change as long as time does not change. Your value is now an invariant in the context of stopped time, but it can never be a constant if there is any context where it does change.

2 comments

"the number 5 is the number 5" isn't so much invariant as axiomatic.
>the value of PI is a constant

You mean "about 3" right?