#MathSky
A polynomial ring is the collection of *finite linear combinations of monomials*; equivalently, the collection of *lin combs of finite-degree monomials* when the no. of indeterminates is finite. However, when there's infinitely many indeterminates, this equivalence doesn't hold, and the
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A polynomial ring is the collection of *finite linear combinations of monomials*; equivalently, the collection of *lin combs of finite-degree monomials* when the no. of indeterminates is finite. However, when there's infinitely many indeterminates, this equivalence doesn't hold, and the
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Comments
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is not an element of the polynomial ring
K[X1,X2,X3,X4,...]
because there's infinitely many linearly-independent (over K) terms. But it's an element of the other ring in question since all of the terms have finite degree.
You can realize it as the inverse limit of polynomial rings in the category of *graded* rings