If I have that A is an open interval the from the definition I have that can I say that ?

thanks for any help

ps sorry about the first post I sent it from my phone and clearly something went wrong sorry

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- October 3rd 2011, 08:07 AMhmmmmsubset question
If I have that A is an open interval the from the definition I have that can I say that ?

thanks for any help

ps sorry about the first post I sent it from my phone and clearly something went wrong sorry - October 3rd 2011, 08:09 AMPlatoRe: subset question
- October 3rd 2011, 09:05 AMhmmmmRe: subset question
sorry about the mistake I made above edited now

- October 3rd 2011, 09:15 AMPlatoRe: subset question
- October 3rd 2011, 11:31 AMhmmmmRe: subset question
yeah it isn't, however we can always choose an r so that it is?

- October 3rd 2011, 12:08 PMPlatoRe: subset question
- October 3rd 2011, 03:19 PMhmmmmRe: subset question
If A is an open subset then

proof

Assume that .

Then as A is open from the definition we have that for

.

Contradiction- as we assumed that but .

I was asking if I can always choose an r such that ?

Thanks for any help - October 3rd 2011, 03:32 PMPlatoRe: subset question
- October 4th 2011, 01:45 AMhmmmmRe: subset question
Is my proof of this statement then correct, specifically where I derived the contradiction and said ?

- October 4th 2011, 03:05 AMPlatoRe: subset question