Dedekind

[ dey-di-kind; German dey-duh-kint ]

Phonetic (Standard)IPA

noun

Ju·li·us Wil·helm Rich·ard [jool, -y, uh, s , wil, -helm , rich, -erd, yoo, -lee-, oo, s , vil, -helm , rikh, -ah, r, t], 1831–1916, German mathematician.

Dedekind

/ ˈdedəˌkɪnt /

Dedekind(Julius Wilhelm) Richard18311916MGermanSCIENCE: mathematician ( Julius Wilhelm ) Richard (ˈjuːlɪʊs ˈvɪlhɛlm ˈrixɑːt). 1831–1916, German mathematician, who devised a way (the Dedekind cut ) of according irrational and rational numbers the same status

It follows from axioms 1-12 by projection that the Dedekind property is true for all lines.

The last axiom of order is that there exists at least one straight line for which the point order possesses the Dedekind property.

An open series is continuous if it is compact and possesses the Dedekind property.

Thus the definitions of compactness and of the Dedekind property can be at once transferred to a closed series.

The Dedekind property holds for the order of the points on any straight line.

April 19, 2024tortuous

[tawr-choo-uhs ]

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