- #1
rbzima
- 83
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I'm trying to prove
\bigcap^{\infty}_{n=1}(0,1/n) = EMPTY SET.
One thing that I can't seem to bypass is getting past the closed intervals as stated in the Nested Interval Property, which states "For each n\in N, assume we are given a closed interval I_n = [a_n, b_n] = {x \in R : a_n \leq x \leq b_n}. Assume also that each I_n contains I_n_+_1.
Therefore, \bigcap^{\infty}_{n=1}I_n \neq EMPTY SET.
Basically, I'm stuck at taking care of the open interval part of this proof. The original for R was proved by showing sup A = x, then x is between the closed interval. Any advice would be great!
\bigcap^{\infty}_{n=1}(0,1/n) = EMPTY SET.
One thing that I can't seem to bypass is getting past the closed intervals as stated in the Nested Interval Property, which states "For each n\in N, assume we are given a closed interval I_n = [a_n, b_n] = {x \in R : a_n \leq x \leq b_n}. Assume also that each I_n contains I_n_+_1.
Therefore, \bigcap^{\infty}_{n=1}I_n \neq EMPTY SET.
Basically, I'm stuck at taking care of the open interval part of this proof. The original for R was proved by showing sup A = x, then x is between the closed interval. Any advice would be great!
