(Class notes for ECE302, Spring 2013, Boutin) |
|||
| Line 22: | Line 22: | ||
Is <math>\mathbb{Z}</math> routable? yes. | Is <math>\mathbb{Z}</math> routable? yes. | ||
| − | + | <math>\mathbb{Z}</math>={0,1,-1,2,-2,3,-3, }as opposed to <math>\mathbb{R}</math> | |
| − | = {0,3,e,<math>\pi</math>,-1,1.14,<math>\sqrt{2}</math>} | + | <math>\mathbb{R}</math>= {0,3,e,<math>\pi</math>,-1,1.14,<math>\sqrt{2}</math>} |
Many different ways to write a set | Many different ways to write a set | ||
[0,1] = {x <math>\in \mathbb{R} </math>such that(s. t.) 0<math>\leq x \leq</math> 1} | [0,1] = {x <math>\in \mathbb{R} </math>such that(s. t.) 0<math>\leq x \leq</math> 1} | ||
={real positive numbers no greater than 1 as well as 0} | ={real positive numbers no greater than 1 as well as 0} | ||
Revision as of 17:06, 14 April 2013
If S is discrete and finite S = {$ s_1,s_2,s_3 $} S = {head,tail} S = {win, lose} S = {1,2,3,4,5,6}
1/9/13
S = {$ s_1,s_2,s_3 $}
If S is discrete but infinite,
S = {$ s_1,s_2,s_3 $,...} ex. S = {1,2,3,4,...}
S = {sin(2$ \pi $*440t),sin(2$ \pi $*880t),sin(2$ \pi $*1320t),...}
Observe $ _{S = \mathbb{R}} $ is not routable; S = [0,1] is not routable
S = {sin(2$ \pi $*f*t)} f $ \in \mathbb{R} \geq $ 0
= {sin(2$ \pi $*f*t)|0$ \leq f < \infty $}
$ \mathbb{Z} $ is all integers $ -\infty $ to $ \infty $ 
Is $ \mathbb{Z} $ routable? yes.
$ \mathbb{Z} $={0,1,-1,2,-2,3,-3, }as opposed to $ \mathbb{R} $
$ \mathbb{R} $= {0,3,e,$ \pi $,-1,1.14,$ \sqrt{2} $}
Many different ways to write a set [0,1] = {x $ \in \mathbb{R} $such that(s. t.) 0$ \leq x \leq $ 1} ={real positive numbers no greater than 1 as well as 0}
