Recent content by Uiiop

ok here is my revised attempt at the answer with your help: In order to prove that (X⊕Y)⊕(Y⊕Z) = X⊕Z you must imply that ⊕ forms a group operation this proof is split up into three parts The symmetric difference is associative which means that (X⊕Y)⊕(Y⊕Z)= (Y⊕Y)⊕(X⊕Z) --I think that...

this is what i think i need to show http://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Venn_0110_1001.svg/200px-Venn_0110_1001.svg.png

Homework Statement There is a symmetric difference in sets X & Y, X Y is defined to be the sets of elements that are either X or Y but not both Prove that for any sets X,Y & Z that (X\oplusY)\oplus(Y\oplusZ) = X\oplusZ Homework Equations \oplus = symmetic difference The Attempt at...

or is it: {(0)union(-1,1)union(-2,2)union(-3,3)union(-4,4)union(-5,5)...}

for 4) {x : x is a real number strictly between − i and i}. would it be: a0 {0} a1 {-1,1} a2 {-2,2} a3 {-3,3} a4 {-4,4} a5 {-5,5} union: {0,-1,1,-2,2,-3,3,-4,4,-5,5,...} intersection: empty set correct?

no i do not... so would a0 then be {(0, 1),...} etc then would the union be {(0,1),(1,2),(2,3),(3,4),(4,5),(5,6),...} or {0,1,2,3,4,5,6,...} i imagine the intersection would be \emptyset whichever way

...ok now I am stuck on 3) {x : x is a real number such that i < x < i + 1} how do you list the x? do you have to declare it? or do you just leave it as x i think I am barking up the wrong tree but this is what i have got thus far... a0 = {0,x,1,...} a1 = {1,x,2,...} a2 = {2,x,3,...} a3 =...

thanks guys i should be ok now no doubt ill be back for help on something else

for 2) Ai = {0, i, 2i} A0 {0,0,0} A1 {0,1,2} A2 {0,2,4} A3 {0,3,6} A4 {0,4,8} A5 {0,5,10} Would \bigcup_{i=0}^{\infty} A_{i} simply be {0,1,2,3,4,5,6,8,10} would \bigcap_{i=0}^{\infty} A_{i} be {0}?

Would \bigcup_{i=0}^{\infty} A_{i} simply be {0,1,-1,2,-2,3,-3,4,-4,5,-5,6,-6,7,-7,...} ? would \bigcap_{i=0}^{\infty} A_{i} be {\o}?

as i said clueless ;D A2 {2,-2,3,-3,4,-4,...} A3 {3,-3,4,-4,5,-5,...} A4 {4,-4,5,-5,6,-6,...} A5 {5,-5,6,-6,7,-7,...}

A2 {0,1,-1,2,-2,3,...} a3 {1,-1,2,-2,3...} a4 {0,1,-1,2,-2,3,-3,...} a5 {1,-1,2,-2,3,-3,...} ?

ok 1) A0 {0,1,-1,2,-2,...} A1 {1,-1,2,-2,...} A2 {-1,2,-2,...} A4 {2,-2,...} A5 {-2,...} think that right probably not... Would \bigcup_{i=0}^{\infty} A_{i} simply be {0,1,-1,2,-2,...} ? would \bigcup_{i=0}^{\infty} A_{i} be {-2,...}?

...ok i need to find \bigcup_{i=0}^{\infty} A_{i} & the \bigcap_{i=0}^{\infty} A_{i} for each i can see that A0 is a set of integers would the union be? A0 \bigcup_ A1 = {0,1,-1,2,-2,...} and the intersection? A0 \bigcap_ A1 = {1,-1,2,-2,...} is that it for question one...

Homework Statement Find ∪i=0Ai (with infinite symbol) and ∩ i=0Ai (with infinite symbol) in each of the cases when for each natural number i, Ai is defined as: 1. Ai = {i,−i, i + 1,−(i + 1), i + 2,−(i + 2), . . .} 2. Ai = {0, i, 2i} 3. Ai = {x : x is a real number such that i < x...