An infinite [dimensional](Hilbert%20space%20dimension.md) [[Hilbert space]], $\mathcal{H}$ is an [$L^2(I)$ space](L2(I)%20space.md), that is, a space of square integral functions. --- # Proofs and Examples ## Proof that infinite dimensional Hilbert Spaces are complete #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/VectorSpaces #MathematicalFoundations/Analysis/FunctionalAnalysis