How to Prove the Empty Intersection of Infinite Intervals?

  • Thread starter Thread starter happybear
  • Start date Start date
happybear
Messages
19
Reaction score
0

Homework Statement


If X = R with a special metirc, En = [n, infinity) ()
How can I show infinite intersection of En is empty?

Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
I am not sure what you mean by "special metric", since the statement you are trying to show has nothing to do with a metric.

To show that the intersection is empty use the fact that for any real number x there exists a positive integer n such that x<n.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Is Y Union A Connected When X Minus Y Splits into Disjoint Subsets A and B?
Replies
39
Views
4K
Intersection of any 2 intervals --> all intervals intersect
Replies
14
Views
2K
Prove that x is in S or x is an accumulation point of S
Replies
25
Views
3K
Proving intersection of finitely many open sets is open
Replies
1
Views
2K
(0,0) Empty Interval? Basic Set Theory
Replies
17
Views
8K
Proving the Empty Intersection of Intervals using Natural Numbers
Replies
3
Views
6K
Prove that an upper bound a is the least upper bound
Replies
11
Views
4K
Prove the diameter of a union of sets is finite
Replies
5
Views
2K
Proving something is not the empty set
Replies
3
Views
2K
Countably Compact: Necessity & Sufficiency
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top