Order structure of real numbers
Set
definiendum | ⟨R,≤⟩ |
We define the total order over the real numbers (in the Dedekind cut model) via r<s≡r⊂s, i.e.
postulate | s⊆r⇔s≥r |
Theorems
Inequality of arithmetic and geometric means (AM-GM inequality):
1n∑nk=1xk≥(∏nk=1xk)1n |
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Reference
Wikipedia: Real number, Construction of the real numbers, Dedekind cut, Inequality of arithmetic and geometric means