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$P\implies Q$ ��

not

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and

not

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�� 3.1

$\displaystyle \forall \epsilon >0 \exists \delta >0 \forall x \in$ $\displaystyle \mbox{${\mathbb{R}}$}$ $\displaystyle \ (\vert x-3\vert<\delta \implies \vert x^2-9\vert<\epsilon)$

( $x \mapsto x^2$ ��

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$\displaystyle \exists \epsilon >0 \forall \delta >0 \exists x \in$ $\displaystyle \mbox{${\mathbb{R}}$}$ $\displaystyle \ ($ not $\displaystyle (\vert x-3\vert<\delta \implies \vert x^2-9\vert<\epsilon))$

(��)

( $x \mapsto x^2$ ��

��Ϣ³�Ǥʤ��Ȥ��̿��(��)) �Ǥ��롣 ��Τ褦�ˡ� $\forall$ �� $\exists$ ��ߤ��̿��ϡ�

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$\forall$ �� $\exists$ ��ؤ��
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�Ȥ��³��롣

��ˡ�̿��(��)�ϡ�(��P $\implies$ Q�פ��꤬ �� and( not )�� Ǥ��ä��Ȥ��顢)

$\displaystyle \exists \epsilon >0 \forall \delta >0 \exists x \in$ $\displaystyle \mbox{${\mathbb{R}}$}$ $\displaystyle (\vert x-3\vert<\delta$ and $% latex2html id marker 970 $\displaystyle \vert x^2-9\vert\geq \epsilon) $$

�Ƚ񤭴��롣

�� 3.2 �Ĥ��γơ��̿��򤽤줾��Ҥ٤ʤ��

$\forall x \in$ $\mbox{${\mathbb{R}}$}$ $\exists y \in$ $\mbox{${\mathbb{R}}$}$
$\forall x \in$ $\mbox{${\mathbb{R}}$}$ $\forall z \in$ $\mbox{${\mathbb{R}}$}$ $\exists y \in$ $\mbox{${\mathbb{R}}$}$ $% latex2html id marker 989 $ \ (x y\neq z) $$