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Diffstat (limited to 'Master/texmf-dist/doc/latex/stex/example/paper/continuous.omdoc')
-rw-r--r-- | Master/texmf-dist/doc/latex/stex/example/paper/continuous.omdoc | 53 |
1 files changed, 53 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/stex/example/paper/continuous.omdoc b/Master/texmf-dist/doc/latex/stex/example/paper/continuous.omdoc new file mode 100644 index 00000000000..19c248a26dd --- /dev/null +++ b/Master/texmf-dist/doc/latex/stex/example/paper/continuous.omdoc @@ -0,0 +1,53 @@ +<?xml version="1.0"?> +<!--This OMDoc document is generated from an sTeX-encoded one via LaTeXML, you may want to reconsider editing it.--> +<omdoc xmlns:omdoc="http://omdoc.org/ns" xmlns="http://omdoc.org/ns" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:stex="http://kwarc.info/ns/sTeX" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns" xmlns:om="http://www.openmath.org/OpenMath"> + <omdoc:omgroup layout="sectioning" xml:id="sec.contfuncs" about="#sec.contfuncs" stex:srcref="continuous.tex#textrange(from=1;0,to=16;13)"> + <omdoc:metadata xml:id="sec.contfuncs.metadata1" about="#sec.contfuncs.metadata1" stex:srcref="continuous.tex#textrange(from=1;0,to=15;12)"> + <dc:title xml:id="sec.contfuncs.metadata1.title1" about="#sec.contfuncs.metadata1.title1" stex:srcref="continuous.tex#textrange(from=1;0,to=16;13)">Continuous Functions</dc:title> + </omdoc:metadata> + <theory xml:id="continuous" about="#continuous" stex:srcref="continuous.tex#textrange(from=2;0,to=15;12)"> + <imports from="../../../slides/extcds/omstd/arith1.omdoc#arith1"/> + <imports from="../../../slides/extcds/omstd/relation1.omdoc#relation1"/> + <omdoc:imports from="../background/functions.omdoc#functions" xml:id="continuous.imports1" about="#continuous.imports1" stex:srcref="continuous.tex#textrange(from=3;0,to=3;46)"/> + <omdoc:imports from="../background/reals.omdoc#reals" xml:id="continuous.imports2" about="#continuous.imports2" stex:srcref="continuous.tex#textrange(from=4;0,to=4;38)"/> + <omdoc:symbol name="continuousfunctions" xml:id="continuousfunctions.sym" about="#continuousfunctions.sym" stex:srcref="continuous.tex#textrange(from=5;1,to=5;54)"/> + <omdoc:notation cd="continuous" name="continuousfunctions"> + <omdoc:prototype> + <om:OMA> + <om:OMS cd="continuous" cr="fun" name="continuousfunctions"/> + <omdoc:expr name="arg1"/> + <omdoc:expr name="arg2"/> + </om:OMA> + </omdoc:prototype> + <omdoc:rendering> + <m:mrow> + <m:msup> + <m:mi mathvariant="script">C</m:mi> + <m:mn>0</m:mn> + </m:msup> + <m:mo>⁢</m:mo> + <m:mfenced open="(" close=")"> + <m:mrow> + <render name="arg1"/> + <m:mo>,</m:mo> + <render name="arg2"/> + </m:mrow> + </m:mfenced> + </m:mrow> + </omdoc:rendering> + </omdoc:notation> + <omdoc:symbol name="continuous" xml:id="continuous.def.sym" about="#continuous.def.sym" stex:srcref="continuous.tex#textrange(from=7;0,to=14;16)"/> + <omdoc:symbol name="continuous-on" xml:id="continuous-on.def.sym" about="#continuous-on.def.sym" stex:srcref="continuous.tex#textrange(from=7;0,to=14;16)"/> + <omdoc:definition for="continuousfunctions continuous continuous-on" xml:id="continuous.definition6" about="#continuous.definition6" stex:srcref="continuous.tex#textrange(from=7;0,to=14;16)"> + <omdoc:CMP xml:id="continuous.definition6.CMP1" about="#continuous.definition6.CMP1" stex:srcref="continuous.tex#textrange(from=7;0,to=14;16)"> + <p xmlns="http://www.w3.org/1999/xhtml" style="" class="p" id="continuous.definition6.CMP1.p1">A function <om:OMOBJ><om:OMA><om:OMS cd="functions" name="fun"/><om:OMV name="f"/><om:OMS cd="reals" name="RealNumbers"/><om:OMS cd="reals" name="RealNumbers"/></om:OMA></om:OMOBJ> is called <omdoc:idx xml:id="continuous.definition6.CMP1.p1.idx2" about="#continuous.definition6.CMP1.p1.idx2" stex:srcref="continuous.tex#textrange(from=7;4,to=8;75)"><omdoc:idt xml:id="continuous.definition6.CMP1.p1.idx2.idt1" about="#continuous.definition6.CMP1.p1.idx2.idt1" stex:srcref="continuous.tex#textrange(from=7;4,to=8;75)"><omdoc:term cd="continuous" name="continuous" role="definiendum" xml:id="continuous.definition6.CMP1.p1.idx2.idt1.term1" about="#continuous.definition6.CMP1.p1.idx2.idt1.term1" stex:srcref="continuous.tex#textrange(from=7;4,to=8;75)">continuous</omdoc:term></omdoc:idt><omdoc:ide index="default" xml:id="continuous.definition6.CMP1.p1.idx2.ide2" about="#continuous.definition6.CMP1.p1.idx2.ide2" stex:srcref="continuous.tex#textrange(from=7;4,to=8;75)"><omdoc:idp>continuous</omdoc:idp></omdoc:ide></omdoc:idx> at +<om:OMOBJ><om:OMA><om:OMS cd="functions" name="inset"/><om:OMV name="x"/><om:OMS cd="reals" name="RealNumbers"/></om:OMA></om:OMOBJ>, iff for all <om:OMOBJ><om:OMA><om:OMS cd="relation1" name="gt"/><om:OMV name="ϵ"/><om:OMI>0</om:OMI></om:OMA></om:OMOBJ> there is a <om:OMOBJ><om:OMA><om:OMS cd="relation1" name="gt"/><om:OMV name="δ"/><om:OMI>0</om:OMI></om:OMA></om:OMOBJ>, such that +<om:OMOBJ><om:OMA><om:OMS cd="relation1" name="lt"/><om:OMA><om:OMS cd="reals" name="absval"/><om:OMA><om:OMS cd="arith1" name="minus"/><om:OMA><om:OMS cd="arith1" name="times"/><om:OMV name="f"/><om:OMV name="x"/></om:OMA><om:OMA><om:OMS cd="arith1" name="times"/><om:OMV name="f"/><om:OMV name="y"/></om:OMA></om:OMA></om:OMA><om:OMV name="ϵ"/></om:OMA></om:OMOBJ> for all <om:OMOBJ><om:OMA><om:OMS cd="relation1" name="lt"/><om:OMA><om:OMS cd="reals" name="absval"/><om:OMA><om:OMS cd="arith1" name="minus"/><om:OMV name="x"/><om:OMV name="y"/></om:OMA></om:OMA><om:OMV name="δ"/></om:OMA></om:OMOBJ>. It is called +<omdoc:idx xml:id="continuous.definition6.CMP1.p1.idx8" about="#continuous.definition6.CMP1.p1.idx8" stex:srcref="continuous.tex#textrange(from=10;60,to=11;25)"><omdoc:idt xml:id="continuous.definition6.CMP1.p1.idx8.idt1" about="#continuous.definition6.CMP1.p1.idx8.idt1" stex:srcref="continuous.tex#textrange(from=10;60,to=11;25)"><omdoc:term cd="continuous" name="continuous-on" role="definiendum" xml:id="continuous.definition6.CMP1.p1.idx8.idt1.term1" about="#continuous.definition6.CMP1.p1.idx8.idt1.term1" stex:srcref="continuous.tex#textrange(from=10;60,to=11;25)">continuous on</omdoc:term></omdoc:idt><omdoc:ide index="default" xml:id="continuous.definition6.CMP1.p1.idx8.ide2" about="#continuous.definition6.CMP1.p1.idx8.ide2" stex:srcref="continuous.tex#textrange(from=10;60,to=11;25)"><omdoc:idp>continuous</omdoc:idp><omdoc:idp>on</omdoc:idp></omdoc:ide></omdoc:idx> a set <om:OMOBJ><om:OMA><om:OMS cd="functions" name="sseteq"/><om:OMV name="S"/><om:OMS cd="reals" name="RealNumbers"/></om:OMA></om:OMOBJ>, iff is is continous at all +<om:OMOBJ><om:OMA><om:OMS cd="functions" name="inset"/><om:OMV name="x"/><om:OMV name="S"/></om:OMA></om:OMOBJ>, the set of all such functions is denoted with <om:OMOBJ><om:OMA><om:OMS cd="continuous" name="continuousfunctions"/><om:OMV name="S"/><om:OMV name="T"/></om:OMA></om:OMOBJ>, +if <om:OMOBJ><om:OMA><om:OMS cd="functions" name="sseteq"/><om:OMA><om:OMS cd="arith1" name="times"/><om:OMV name="f"/><om:OMV name="S"/></om:OMA><om:OMV name="T"/></om:OMA></om:OMOBJ>.</p> + </omdoc:CMP> + </omdoc:definition> + </theory> + </omdoc:omgroup> +</omdoc> |