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Revision as of 15:50, 31 January 2009
, 15:50, 31 January 2009→Definition 6: format + reformulate a bit
===Definition 6===
===Definition 6===
<pre>
<br>
If Sj is a sentence
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"
|
{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px; text-align:center"
| width="80%" |
| width="20%" | <math>\text{Definition 6}\!</math>
|}
|-
|
{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:60px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="80%" style="border-top:1px solid black" |
<p><math>s_j ~\text{is a sentence about things in the universe}~ X</math></p>
<p><math>\text{for each}~ j \in J</math></p>
|- style="height:40px"
|
| <math>\text{then}\!</math>
| <math>\text{the following are equivalent:}\!</math>
|}
|-
|
{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\operatorname{D6a.}</math>
| width="80%" style="border-top:1px solid black" | <math>s_j, ~\operatorname{for~all}~ j \in J</math>
|- style="height:40px"
|
| <math>\operatorname{D6b.}</math>
| <math>\forall_{j \in J} s_j</math>
|- style="height:40px"
|
| <math>\operatorname{D6c.}</math>
| <math>\forall_j^J s_j</math>
|- style="height:40px"
|
| <math>\operatorname{D6d.}</math>
| <math>\operatorname{Conj}_{j \in J} s_j</math>
|- style="height:40px"
|
| <math>\operatorname{D6e.}</math>
| <math>\operatorname{Conj}_j^J s_j</math>
|}
|}
<br>
</pre>
===Definition 7===
===Definition 7===
