
#1
Jun3008, 02:10 AM

P: 199

For the set A = {1,2,3,4,5,6,7}, determine whether script A is a partition of A. script A = {{1,3,},{5,6}, {2,4},{7}}
Describe the partition for the equivalence relation T defined for x,y [tex] \in \mathbbc{R} [/tex] by X T y iff [tex] \left[ \left[x \right] \right] = \left[ \left[y \right] \right] where \left[ \left[x \right] \right] [/tex] is definied to be the greatest integer iin x (the largest integer n such that n [tex] \leq [/tex] x). Can anyone help me with this partition stuff. It would be very appreciated. :) 



#2
Jun3008, 02:59 AM

Sci Advisor
HW Helper
P: 4,301

Can you start by giving the definition of a partition?
Then try to check if the given sets [itex]A, \mathcal{A}[/itex] satisfy this definition. For the second one, can you imagine what the equivalence classes look like? 



#3
Jun3008, 06:47 AM

P: 199

(i) If X [tex] \in \mathcal{A}, [/tex] then X [tex] \neq \o [/tex]
(ii) If X [tex] \in \mathcal{A} [/tex] and Y [tex]\in \mathcal{A}[/tex], then X=Y or X [tex]\cap [/tex] Y= [tex]\o[/tex] (iii)[tex]\bigcup_{X \in \mathal{A}}X=A[/tex] I found this to be a definition for an equivalence class: In mathematics, given a set X and an equivalence relation ~ on X, the equivalence class of an element a in X is the subset of all elements in X which are equivalent to a: [tex]\left[a\right]={x \in Xx \sim a} [/tex] 



#4
Jun3008, 08:10 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,877

PartitionsNow try some examples. What numbers are equivalent to 0? to 1/2? to 5/4? to [itex]\pi[/itex]? 



#5
Jun3008, 08:32 AM

P: 199

All the numbers in a subset are only in one subset once.
What do you mean by what numbers are equivalent to 0, 1/2, pi, etc 


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