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If S is discrete and finite
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<br> 1/9/13 <br>
S = {,,}
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<!-- \mathbb{} is used to get the "mathbook" font introduced within the math function-->
S = {head,tail}
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<math>\mathbb{}\text{If S is discrete and finite S = }  \{S_1, S_2, S_3\}, \text{ S = }  \{head,tail\}, S = \{win, lose\}, S = \{1,2,3,4,5,6\}</math>
S = {win, lose}
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<br><math>\mathbb{}\text{If S is discrete but infinite, S = } \{S_1,S_2,S_3,...\}. \text{ Example: S = }\{1,2,3,4,...\} </math>
S = {1,2,3,4,5,6}
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<br><math>\mathbb{}\text{S = }\{\sin(2\pi*440t),\sin(2\pi*880t),\sin(2\pi*1320t),...\}</math>
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<br><math>\mathbb{}\text{Observe }\text{S = }\{\mathbb{R}\} \text{ is not routable; S = }\{0,1\} \text{ is not routable.}</math><br><math>\mathbb{}\text{S = } f \in \mathbb{R} \geq 0</math>
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<br><math>\mathbb{}\text{S = }\{\sin(2\pi*f*t) \mid 0 \leq f \leq \infty \}</math>
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<br><math>\mathbb{Z} \text{ is all integers -}\infty \text{ to } \infty</math>  
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<br><math>\text{Is } \mathbb{Z} \text{ routable? yes.}</math>
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<br><math>\mathbb{Z} = \{ 0,1,-1,2,-2,3,-3,... \}  \text{ as opposed to } \mathbb{R}</math>
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<br><math>\mathbb{R} = \{0,3,e,\pi ,-1,1.14,\sqrt{2}\}</math>
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<br><math>\mathbb{}\text{Many different ways to write a set } [0,1] \text{ = }  \{ x \in \mathbb{R} \text{ such that (s. t.) } 0\leq x \leq 1 \} </math>
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<br><math>\mathbb{} = \{ \text{real positive numbers no greater than 1 as well as 0} \} </math>
  
1/9/13
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[[Image:100 3.jpg|500x700px]]
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[[Image:100 4.jpg|500x700px]]
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[[Image:100 5.jpg|500x700px]]
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<br>
  
Quizzes: use {}
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----
  
S = <math> s\exp{1} <\math>
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Go to lecture notes: [[ECE302S13Notes|2]] [[302L3|3]] [[302L4|4]] [[302L6|6]] [[302L7|7]] [[302L8|8]] [[302L9|9]] [[302L10|10]] [[302L12|12]] [[302L18|18]] [[302L20|20]] [[302L32|32]] [[302L35|35]] [[302L37|37]] [[302L38|38]] [[302L39|39]] [[302L40|40]] [[302L41|41]] [[302L42|42]] [[302L43|43]] [[302L44|44]]
 
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IF S is discrete but infinite,
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S = {,,,....}
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ex.  S = {1,2,3,4,...}
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      S = {sin(2*440t),sin(2*880t),sin(2*1320t),...}
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Observe S = is not routable; S = [0,1] is not routable
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S = {sin(2*f*t)}  =
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{sin(2*f*t)|0}
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is all integers -to 
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Is routable? yes. 
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={0,1,-1,2,-2,3,-3, }as opposed to 
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= {0,3,e,,-1,1.14,, }
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Many different ways to write a set
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[0,1] = {xsuch that(s. t.) 0x 1}
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={real positive numbers no greater than 1 as well as 0}
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Latest revision as of 21:26, 13 May 2014


1/9/13
$ \mathbb{}\text{If S is discrete and finite S = } \{S_1, S_2, S_3\}, \text{ S = } \{head,tail\}, S = \{win, lose\}, S = \{1,2,3,4,5,6\} $
$ \mathbb{}\text{If S is discrete but infinite, S = } \{S_1,S_2,S_3,...\}. \text{ Example: S = }\{1,2,3,4,...\} $
$ \mathbb{}\text{S = }\{\sin(2\pi*440t),\sin(2\pi*880t),\sin(2\pi*1320t),...\} $
$ \mathbb{}\text{Observe }\text{S = }\{\mathbb{R}\} \text{ is not routable; S = }\{0,1\} \text{ is not routable.} $
$ \mathbb{}\text{S = } f \in \mathbb{R} \geq 0 $
$ \mathbb{}\text{S = }\{\sin(2\pi*f*t) \mid 0 \leq f \leq \infty \} $
$ \mathbb{Z} \text{ is all integers -}\infty \text{ to } \infty $
$ \text{Is } \mathbb{Z} \text{ routable? yes.} $
$ \mathbb{Z} = \{ 0,1,-1,2,-2,3,-3,... \} \text{ as opposed to } \mathbb{R} $
$ \mathbb{R} = \{0,3,e,\pi ,-1,1.14,\sqrt{2}\} $
$ \mathbb{}\text{Many different ways to write a set } [0,1] \text{ = } \{ x \in \mathbb{R} \text{ such that (s. t.) } 0\leq x \leq 1 \} $
$ \mathbb{} = \{ \text{real positive numbers no greater than 1 as well as 0} \} $

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