- #1

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R\Q={a+Q:? <a<?}

a€R but if it is not bounded then it will repeat

please help me

n

- Thread starter matness
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- #1

- 90

- 0

R\Q={a+Q:? <a<?}

a€R but if it is not bounded then it will repeat

please help me

n

- #2

matt grime

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you define [x]+[y] to be [x+y] wehre [z] means the equivalence class of y (ie the coset y+Q)

- #3

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for example R\Z ={x+Z: 0<x<1} is set of disjoint sets

so can we also find conditions for y to be disjoint and nice?

- #4

matt grime

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- #5

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probably. sorry for misremembering the defn for cyclic groups

what i want to know is a description for set of disjoint (but not same) cosets such that their union is real numbers.

the R\Q question crossed my mind because of the description R\Z ={x+Z: 0<x<1} if x were bounded as 0<x<2 some of the elements of the R\Z would be same That is what i mean by "repetition".

but i could'nt describe a set for R\Q in the same way

All of these seemed to me related to counting. when counting real numbers(it is a bit utopian) adding a number € Z and a real number between 0 and 1 is enough. (e.g. 3.4=3+0.4 and this representation is unique using this method)

but same method using rational numbers does not work ,

can we say adding a number € Q and an irrational number between 0 and 1 is enough .

(a real number is more than enough)

thanks in advance

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