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\lim_{n\rightarrow\infty} x^n=0\ \mbox{pointwise}\ \mbox{on}\ \mbox{the}\ \mbox{interval}\ [0,1),\ \mbox{but}\ \mbox{not}\ \mbox{uniformly}\ \mbox{on}\ \mbox{the}\ \mbox{interval}\ [0,1).

LaTeXML (experimental; uses MathML) rendering

MathML (10.838 KB / 1.516 KB) :

lim n → ∞ ⁡ x n = 0 ⁢ pointwise ⁢ on ⁢ the ⁢ interval ⁢ [ 0 , 1 ) , but ⁢ not ⁢ uniformly ⁢ on ⁢ the ⁢ interval ⁢ [ 0 , 1 ) . subscript → 𝑛 superscript 𝑥 𝑛 0 pointwise on the interval 0 1 but not uniformly on the interval 0 1 {\displaystyle\lim_{{n\rightarrow\infty}}x^{n}=0\ {\mbox{pointwise}}\ {\mbox{% on}}\ {\mbox{the}}\ {\mbox{interval}}\ [0,1),\ {\mbox{but}}\ {\mbox{not}}\ {% \mbox{uniformly}}\ {\mbox{on}}\ {\mbox{the}}\ {\mbox{interval}}\ [0,1).} 
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limit Underscript n right-arrow normal infinity Endscripts x Superscript n Baseline equals 0 times pointwise times on times the times interval times left-bracket 0 comma 1 right-parenthesis comma but times not times uniformly times on times the times interval times left-bracket 0 comma 1 right-parenthesis period

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lim n → ∞ x n = 0   pointwise   on   the   interval   [ 0 , 1 ) ,   but   not   uniformly   on   the   interval   [ 0 , 1 ) . {\displaystyle \lim _{n\rightarrow \infty }x^{n}=0\ {\mbox{pointwise}}\ {\mbox{on}}\ {\mbox{the}}\ {\mbox{interval}}\ [0,1),\ {\mbox{but}}\ {\mbox{not}}\ {\mbox{uniformly}}\ {\mbox{on}}\ {\mbox{the}}\ {\mbox{interval}}\ [0,1).} 
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    <annotation encoding="application/x-tex">{\displaystyle \lim _{n\rightarrow \infty }x^{n}=0\ {\mbox{pointwise}}\ {\mbox{on}}\ {\mbox{the}}\ {\mbox{interval}}\ [0,1),\ {\mbox{but}}\ {\mbox{not}}\ {\mbox{uniformly}}\ {\mbox{on}}\ {\mbox{the}}\ {\mbox{interval}}\ [0,1).}</annotation>
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SVG (18.462 KB / 6.525 KB) :

{\displaystyle \lim _{n\rightarrow \infty }x^{n}=0\ {\mbox{pointwise}}\ {\mbox{on}}\ {\mbox{the}}\ {\mbox{interval}}\ [0,1),\ {\mbox{but}}\ {\mbox{not}}\ {\mbox{uniformly}}\ {\mbox{on}}\ {\mbox{the}}\ {\mbox{interval}}\ [0,1).}

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