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- Q1065257-06573551-4cbe-e5f4-ded2-1a02ea7445e7 type BestRank @default.
- Q1065257-06573551-4cbe-e5f4-ded2-1a02ea7445e7 type Statement @default.
- Q1065257-06573551-4cbe-e5f4-ded2-1a02ea7445e7 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \forall a,b,c\in \mathbb {R} ^{\mathbb {N} }\colon \left(\left(\lim _{n\to \infty }a_{n}=\lim _{n\to \infty }c_{n}\land \forall n\colon a_{n}\leq b_{n}\leq c_{n}\right)\implies \lim _{n\to \infty }b_{n}=\lim _{n\to \infty }a_{n}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀<!-- ∀ --></mi> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo>∈<!-- ∈ --></mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mrow> </msup> <mo>:<!-- : --></mo> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→<!-- → --></mo> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munder> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→<!-- → --></mo> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munder> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>∧<!-- ∧ --></mo> <mi mathvariant="normal">∀<!-- ∀ --></mi> <mi>n</mi> <mo>:<!-- : --></mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>≤<!-- ≤ --></mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>≤<!-- ≤ --></mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mspace width="thickmathspace" /> <mo stretchy="false">⟹<!-- ⟹ --></mo> <mspace width="thickmathspace" /> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→<!-- → --></mo> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munder> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo stretchy="false">→<!-- → --></mo> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munder> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a,b,c\in \mathbb {R} ^{\mathbb {N} }\colon \left(\left(\lim _{n\to \infty }a_{n}=\lim _{n\to \infty }c_{n}\land \forall n\colon a_{n}\leq b_{n}\leq c_{n}\right)\implies \lim _{n\to \infty }b_{n}=\lim _{n\to \infty }a_{n}\right)}</annotation> </semantics> </math>" @default.