| 31. | Hilbert tied it when he beat Theodore with a long wrist shot.
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| 32. | These do not, technically, belong to the Hilbert space itself.
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| 33. | For separable Hilbert spaces, it is the unique ideal.
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| 34. | Hilbert sent his results to the " Mathematische Annalen ".
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| 35. | Hilbert's approach signaled the shift to the modern axiomatic method.
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| 36. | In 1900, David Hilbert published a famous list of mathematical problems.
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| 37. | Two prominent examples occur for Banach spaces and Hilbert spaces.
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| 38. | Suppose is a compact self-adjoint operator on a Hilbert space.
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| 39. | Let be a bounded self-adjoint operator on a Hilbert space.
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| 40. | Hilbert then states that " mathematics is a presuppositionless science.
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