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An issue with footnotes


Chronological Thread 
  • From: Anderson Brasil <address@hidden>
  • To: address@hidden
  • Subject: An issue with footnotes
  • Date: Mon, 12 Oct 2020 21:41:24 -0300
    Hi. I've just got a new computer and at the process of reinstalling everything I've just migrated textmacs from version 1.99.6 to version 1.99.13. I've noticed that the new version is putting footnotes at strange places. I've attached the tm file and the PDF results created at both versions of texmacs, so you can see by yourself. Is it intended or a bug?

    Thanks in advance [and apologies for this cold murder of the English language],

    Anderson Brasil

Attachment: docAtTexmacsVs1.99.6.pdf
Description: Adobe PDF document

Attachment: docAtTexmacsVs1.99.13.pdf
Description: Adobe PDF document

<TeXmacs|1.99.6>

<style|<tuple|book|portuguese>>

<\body>
  <\strong>
    Disciplina: Lógica e Conjuntos

    Professor: Anderson Brasil

    Período: 1/2020\ 
  </strong>

  <section|Tópicos selecionados sobre conjuntos>

  <\exercise>
    <label|Exerc10>Seja <math|A=<around|{|1, <around|{|2|}>,3,
    <around|{|4|}>, <around|{|5,6, 7|}>, 7|}>>. Determine o que é verdadeiro
    e o que é falso:

    <\with|par-columns|2>
      <\enumerate-alpha>
        <item> <label|Exerc10a><math|1\<in\>A>;

        <item> <label|Exerc10b><math|2\<in\>A>;

        <item> <label|Exerc10c><math|<around|{|2|}>\<in\>A>;

        <item> <label|Exerc10d><math|4<neg|\<in\>>A>;

        <item> <label|Exerc10e><math|<around|{|5,6|}>\<subseteq\>A>;

        <item> <label|Exerc10f><math|<around|{|7|}>\<subseteq\>A>;

        <item> <label|Exerc10g><math|<around|{|1,3|}>\<subseteq\>A>;

        <item> <label|Exerc10h><math|<around|{|<around|{|2|}>,<around|{|4|}>|}>\<subseteq\>A>;
      </enumerate-alpha>
    </with>
  </exercise>

  <\exercise>
    <label|Exerc20>Escrever simbolicamente, de pelo menos duas formas
    distintas, cada um dos conjuntos:

    a) conjunto dos números primos positivos, menores que 43;

    b) conjunto dos números pares compreendidos entre 27 e 30;

    c) conjunto dos números reais cuja quarta potência é 4;

    d) conjunto dos números pares<\footnote>
      Não esqueça de incluir na lista os números pares negativos e o zero.
    </footnote>;

    e) conjunto das raízes reais de <math|x<rsup|2>=9>;

    f) conjunto das raízes reais de <math|x<rsup|2>=-1>;
  </exercise>

  <\exercise>
    <label|Exerc30>Identificar como falso ou verdadeiro:

    a) <math|<around|{|1, 4, 9, 16, 25,\<ldots\>|}>=<around|{|x\<in\>\<bbb-N\>;\<exists\>n\<in\>\<bbb-N\><rsup|\<ast\>>
    \| x=n<rsup|2>|}>>;

    b) <math|<around|{|3,7,11,15|}>={x\<in\>\<bbb-Z\>;x\<geqslant\>3> e
    <math|x\<leqslant\>15> e <math|<frac|x-3|4>\<in\>\<bbb-Z\>>};

    c) <math|<around|{|2,4,6,8,10,\<ldots\>|}>={n\<in\>\<bbb-Z\>;\<exists\>k\<in\>\<bbb-Z\>>
    com <math|n=2k><math|}>;

    d) <math|\<bbb-Q\>=<around*|{|x\<in\>\<bbb-R\>;
    \<exists\>p,q\<in\>\<bbb-N\><rsup|\<ast\>>\|x=<frac|p|q>|}>>;
  </exercise>

  <\exercise>
    <label|Exerc40>Determinar todos os conjuntos:

    <\with|par-columns|2>
      a) <math|<around|{|x\<in\>\<bbb-R\>;x\<neq\>x|}>>;

      b) <math|<around|{|x\<in\>\<bbb-R\>;x=x|}>>;

      c) <math|<around|{|x\<in\>\<bbb-Q\>;<around|\||x|\|>=x|}>>;

      d) <math|<around|{|x\<in\>\<bbb-R\>;\<exists\>y\<in\>\<bbb-R\><rsub|+>\|x=y<rsup|2>|}>>;

      e) <math|<around*|{|x\<in\>\<bbb-R\>;\<exists\>y\<in\>\<bbb-R\> com
      x=y<rsup|2>|}>>;

      f) <math|<around*|{|x\<in\>\<bbb-R\><rsub|->;\<exists\>y\<in\>\<bbb-R\>
      com x=y<rsup|2>|}>>;

      g) <math|<around*|{|x\<in\>\<bbb-R\>;
      \<exists\>p,q\<in\>\<bbb-Z\><rsup|\<ast\>>\|x=<frac|p|q>|}>>;
    </with>
  </exercise>

  <\exercise>
    <label|Exerc160>Se <math|A=<around|{|n\<in\>\<bbb-N\>;\<exists\>x\<in\>\<bbb-N\>\|
    n=4x|}>> e <math|B=\<bbb-R\><rsub|+>> identifique que elementos pertencem
    à <math|A\<times\>B>:

    <\with|par-columns|2>
      a) <math|<around|(|8, -<sqrt|2>|)>>;

      b) <math|<around*|(|3, <frac|1|2>|)>>;

      c) <math|(-4,17)>;

      d) <math|<around|(|16,19|)>>;

      e) <math|<around|(|1, 0|)>>;

      f) <math|<around|(|1000,-1|)>>;
    </with>
  </exercise>

  <\exercise>
    Desenhe o diagrama de Venn de três conjuntos <math|A>, <math|B>, <math|C>
    no conjunto universo e marque <math|A\<cap\>B>, <math|A\<cup\>C>,
    <math|B<rsup|c>>, <math|C-B>, <math|<around|(|A\<cap\>B|)>\<cup\><around|(|A\<cap\>C|)>>
    e <math|<around*|(|A\<cup\>B|)>\<cap\><around|(|A\<cup\>C|)>>.
  </exercise>

  <\exercise>
    O objetivo deste exemplo é ilustrar que diagramas de Venn não funcionam
    bem quando se trabalha com quatro ou mais conjuntos . Observe a figura
    abaixo que, aparentemente, parece ser um diagrama de Venn perfeitamente
    válido para os conjuntos <math|A,B,C> e <math|D>. Mas aonde está o
    conjunto <math|<around*|(|A\<cap\>D|)>-<around*|(|*B\<cup\>C|)>>?
  </exercise>

  <\with|par-mode|center>
    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  </with>

  <\exercise>
    <label|Exerc110>Se <math|A=<around|{|x\<in\>\<bbb-R\>\|0\<leqslant\>x\<leqslant\>4|}>>
    e <math|B=<around|{|x\<in\>\<bbb-R\>\|1\<leqslant\>x\<less\>3|}>>
    determine graficamente o conjunto <math|A-B> e seguida descreva-o a
    partir de uma propriedade.
  </exercise>

  <\exercise>
    <label|Exerc50>Seja <math|A=<around|{|x\<in\>\<bbb-R\>;
    x<rsup|2>\<geqslant\>1|}>>, <math|B=<around|{|x\<in\>\<bbb-R\>;
    \<exists\>m\<in\>\<bbb-N\>,\<exists\>n\<in\>\<bbb-N\><rsup|\<ast\>>\|x=<frac|m|n>|}>>,
    <math|C=<around|{|x\<in\>\<bbb-R\>;\<exists\>q\<in\>\<bbb-Q\>\|x<rsup|3>=q|}>>
    e <math|D=<around*|{|<sqrt|<frac|17|3>|3>, -<frac|1|8>,
    27,-<sqrt|<frac|1|2>|3>|}>>. Determine:

    <\with|par-columns|2>
      a) <math|A\<cap\>D>;

      b) <math|B\<cap\>D>;

      c) <math|C\<cap\>D>.
    </with>
  </exercise>

  <\exercise>
    <label|Exerc60>Sejam <math|A=<around*|{|x\<in\>\<bbb-Q\><mid|\|>x<rsup|2>\<leqslant\>3|}>>,
    <math|B=<around*|{|-3,<sqrt|<frac|1|2>|2>, 1, 2,<sqrt|3|2>, -1|}>> e
    <math|C=><math|<around*|{|x\<in\>\<bbb-Q\>;\<exists\>y\<in\>\<bbb-R\>\|x=y<rsup|2>|}>>
    e <math|D=<around*|{|<sqrt|3>, <frac|9|5>,
    -<frac|1|4>,<frac|4|7>,<frac|50|6>,<frac|16|3>|}>> e
    <math|E=<around*|{|y\<in\>\<bbb-R\>;\<exists\>p,q\<in\>\<bbb-N\><rsup|\<ast\>>\|y=<frac|p<rsup|2>|q>|}>>.
    Determine:

    <\with|par-columns|2>
      a) <math|A\<cap\>B>;

      b) <math|A\<cap\>C>;

      c) <math|B\<cap\>C>;

      d) <math|D\<cap\>E>;

      e) <math|C\<cap\>E>;

      f) <math|B\<cap\>E>;
    </with>
  </exercise>

  <\exercise>
    <label|Exerc70>Sejam <math|A=<left|{>\<nocomma\><frac|1|2>,<sqrt|<frac|1|2>|4>,<around*|{|0,<around*|{|1|}>|}>,<left|{>2,4<left|}>,8<left|}>>,
    <math|B=<around*|{|0,<frac|1|2>,<around*|{|2,4|}>,<around*|{|8|}>|}>>,
    <math|C=<left|{>x\<in\>\<bbb-R\>;\<exists\>y\<in\>\<bbb-Q\><around*|\||x<rsup|2>=y|}>>
    e <math|D=<around*|{|x\<in\>\<bbb-R\>; 3x<rsup|4>\<gtr\>1|}>>. Determine:

    <\with|par-columns|2>
      a) <math|A\<cap\>B>;

      b) <math|A\<cap\>C>;

      c) <math|A\<cap\>D>;
    </with>
  </exercise>

  <\exercise>
    <label|Exerc80>É comum se utilizar a notação
    <math|<around|{|f<around|(|\<lambda\>|)>,\<lambda\>\<in\>\<Lambda\>|}>
    para designar> <math|<around*|{|x;\<exists\>\<lambda\>\<in\>\<Lambda\>\|f<around|(|\<lambda\>|)>=x|}>>
    (considerando-se o conjunto universo subentendido pela situação e que,
    neste curso, geralmente será <math|\<bbb-R\>>). Por exemplo, o conjunto
    dos inteiros pares pode ser denotado por
    <math|<around|{|2n,n\<in\>\<bbb-Z\>|}>>. Se
    <math|A=<around*|{|<frac|1|n>,n\<in\>\<bbb-N\><rsup|\<ast\>>|}>>,
    <math|B=<around*|{|<frac|1|n<rsup|2>>,n\<in\>\<bbb-Q\><rsup|\<ast\>>|}>>,
    <math|C=<around*|{|9x<rsup|2>+27x-5,x\<in\>\<bbb-Q\>|}>> e seja ainda
    <math|D=<around*|{|<frac|1|7>,<sqrt|2>, <frac|1|9>,<frac|1|2>,17, -4
    |}>>. Achar\ 

    <\with|par-columns|2>
      a) <math|A\<cap\>D>;

      b) <math|B\<cap\>D>;

      c) <math|C\<cap\>D>;

      d) <math|A\<cap\>B>.
    </with>
  </exercise>

  <\very-small>
    <strong|Soluções:> <reference|Exerc10>) <reference|Exerc10a>)V;
    <reference|Exerc10b>) F; <reference|Exerc10c>) V; <reference|Exerc10d>)
    V; <reference|Exerc10e>) F; <reference|Exerc10f>) V;
    <reference|Exerc10g>) V; <reference|Exerc10h>) V; <reference|Exerc30>)
    a)V; b) V; c) F; d) F; <reference|Exerc40>) a) <math|\<varnothing\>>; b)
    <math|\<bbb-R\>>; c) <math|\<bbb-Q\><rsub|+>>; d)
    <math|\<bbb-R\><rsub|+>>; e) <math|\<bbb-R\><rsub|+>>; f)
    <math|<around|{|0|}>>; g) <math|\<bbb-Q\><rsup|\<ast\>>>;
    <reference|Exerc160>) Somente d; <reference|Exerc110>)
    <math|{x\<in\>\<bbb-R\>;0\<leqslant\>x\<less\>1> ou
    <math|3\<leqslant\>x\<leqslant\>4}>; <reference|Exerc50>) a)
    <math|<around*|{|<sqrt|<frac|17|3>|3>, 27|}>>; b) <math|<around|{|27|}>>;
    c) <math|<around*|{|<sqrt|<frac|17|3>|3>, -<frac|1|8>,
    27,-<sqrt|<frac|1|2>|3>|}>>; <reference|Exerc60>) a) <math|{-1, 1}>; b)
    <math|<around|{|x\<in\>\<bbb-Q\><rsub|+>;x<rsup|2>\<leqslant\>3|}>>; c)
    <math|<around|{|1,2|}>>; d) <math|<around*|{|<frac|9|5>, <frac|4|7>,
    <frac|50|6>,<frac|16|3>|}>>; e) <math|E>; f) <math|<around|{|1,2|}>>;
    <reference|Exerc70>) a) <math|<left|{><frac|1|2>,<left|{>2,4<left|}><left|}>;>b)
    <math|<around*|{|<frac|1|2>,8|}>>; c)
    <math|<around*|{|<sqrt|<frac|1|2>|4>,8|}>;><reference|Exerc80>)
    a)<math|<around*|{|<frac|1|7>,<frac|1|9>,<frac|1|2>|}>>; b)
    <math|<around*|{|<frac|1|9>|}>>; c) <math|<around|{|17|}>>; d) <math|B>.
  </very-small>
</body>

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    <associate|preamble|false>
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</initial>

<\references>
  <\collection>
    <associate|Exerc10|<tuple|1|1>>
    <associate|Exerc10a|<tuple|a|1>>
    <associate|Exerc10b|<tuple|b|1>>
    <associate|Exerc10c|<tuple|c|1>>
    <associate|Exerc10d|<tuple|d|1>>
    <associate|Exerc10e|<tuple|e|1>>
    <associate|Exerc10f|<tuple|f|1>>
    <associate|Exerc10g|<tuple|g|1>>
    <associate|Exerc10h|<tuple|h|1>>
    <associate|Exerc110|<tuple|8|2>>
    <associate|Exerc160|<tuple|5|1>>
    <associate|Exerc20|<tuple|2|1>>
    <associate|Exerc30|<tuple|3|1>>
    <associate|Exerc40|<tuple|4|1>>
    <associate|Exerc50|<tuple|9|2>>
    <associate|Exerc60|<tuple|10|2>>
    <associate|Exerc70|<tuple|11|2>>
    <associate|Exerc80|<tuple|12|2>>
    <associate|auto-1|<tuple|1|1>>
    <associate|footnote-1|<tuple|1|1>>
    <associate|footnr-1|<tuple|1|1>>
  </collection>
</references>

<\auxiliary>
  <\collection>
    <\associate|toc>
      1<space|2spc>Tópicos selecionados sobre conjuntos
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-1>
    </associate>
  </collection>
</auxiliary>

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