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→Comments: Concerning "The proof of Cantor's second theorem does not state why some limits exist. The proof he was using does." |
Misc cleanup: Removed confusing ref to Dauben in paragraph that printed at bottom of page |
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:The explanation of the fact that you are concerned about is in the following paragraph:
::Kronecker's influence appears in the proof of Cantor's second theorem. Cantor used Dedekind's version of the proof except he left out why the limits ''a''<sub>∞</sub> = lim<sub>''n'' → ∞</sub> ''a<sub>n</sub>'' and ''b''<sub>∞</sub> = lim<sub>''n'' → ∞</sub> ''b<sub>n</sub>'' exist. Dedekind had used his "principle of continuity" to prove they exist. This principle (which is equivalent to the [[least upper bound property]] of the real numbers) comes from Dedekind's construction of the real numbers, a construction Kronecker did not accept.
:If my structuring or explanation is not clear to you, please give me suggestions for modifying them. Thanks, — [[User:RJGray|RJGray]] ([[User talk:RJGray|talk]]) 19:51, 7 August 2018 (UTC)
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