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Revision as of 20:52, 2 February 2009
, 20:52, 2 February 2009→Syntactic Transformation Rules: format definition box
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{| 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%"
Definition 3
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
If f, g : U -> V,
|- style="height:40px; text-align:center"
| width="80%" |
then the following are equivalent:
| width="20%" | <math>\operatorname{Definition~3}</math>
|}
D3a. f = g.
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D3b. f(u) = g(u), for all u C U.
{| align="center" cellpadding="0" cellspacing="0" width="100%"
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|- style="height:40px"
| 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" | <math>f, g ~:~ X \to Y</math>
|- 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{D3a.}</math>
| width="80%" style="border-top:1px solid black" | <math>f ~=~ g</math>
|- style="height:60px"
|
| <math>\operatorname{D3b.}</math>
| <math>\overset{X}{\underset{x}{\forall}}~ (f(x) ~=~ g(x))</math>
|}
|}
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