proofs

given that S=( 0,1), show that the max S doesnt exist.

to show that, my notes states that:

let M ∈ S and M= max S.

take M* = (M+1)/2

then we need to show that M* ∈ S and that M < M*...

mayb i know if there is a fixed method that i can adopt whener i have to solve proving questions?

Quote:

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Originally Posted by alexandrabel90

given that S=( 0,1), show that the max S doesnt exist.
to show that, my notes states that:
let M ∈ S and M= max S.
take M* = (M+1)/2
then we need to show that M* ∈ S and that M < M*...

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This is always true.
If then .

Well suppose there was an with for all . Clearly we would need to have , because all elements of are . Thus the open interval is not empty, and all of its elements are in and all of them are greater than - this clearly contradicts the definition of .