[color=#006600][/color] let Ω=N , the set of all natural numbers. For each {An}n∈N, find U An, ∩ An.


1. An=(0,1/n) open interval






2. An=(0,1/n) half open interval




3. ∑ ∞ r=1 (1/r²)

Geniuses don't exist

Chidorx60:
Geniuses don't exist

Who told u

Need2learnmuch:


Who told u

Life

Chidorx60:
Life

Ok can u help me solve this

The last one, if I am right, is a summation from 1 to infinity of the term 1/r². The answer is π²/6. It was proved my Leonard Euler. The proof is beyond my knowledge of Mathematics.

Martinez39:
The last one, if I am right, is a summation from 1 to infinity of the term 1/r². The answer is π²/6. It was proved my Leonard Euler. The proof is beyond my knowledge of Mathematics.

Thanks for trying but the last answer is

3.U Sa=(3/2) ∩ Sa=(1)


The thing is that I can't solve it

Need2learnmuch:



Thanks for trying but the last answer is

3.U Sa=(3/2) ∩ Sa=(1)


The thing is that I can't solve it

Expect if your "r" meant something else or I didn't get the context of the problem. I am sure that the infinite series Σ (1/r²) converges to π²/6 ie. Σ (1/r²) = π²/6.

Martinez39:
Expect if your "r" meant something else or I didn't get the context of the problem. I am sure that the infinite series Σ (1/r²) converges to π²/6 ie. Σ (1/r²) = π²/6.

But what about 1&2

Need2learnmuch:


Ok can u help me solve this

Nope,too stressful. beside this aint my area of mathematical specialization.

Need2learnmuch:

But what about 1&2

I don't know them.

Martinez39:
The last one, if I am right, is a summation from 1 to infinity of the term 1/r². The answer is π²/6. It was proved my Leonard Euler. The proof is beyond my knowledge of Mathematics.

Really need to find the proof that is beyond the knowledge of Martinez39,
Kudos to Euler the blind genius.

Chidorx60:
Really need to find the proof that is beyond the knowledge of Martinez39, Kudos to Euler the blind genius.

don't forget this is indexing sets question

Need2learnmuch:



don't forget this is indexing sets question

This is point-set topology.

An = (0,1/n), An+1 = (0,1/(n+1))
An+1 is contained in An, so An is contained in An-1 which is contained in An-2 and so on till A1=(0,1), so An is contained in A1 for all n, and so their union is just A1. Intersection of An and Am is max(n,m), intersection from A1 upto an arbitrary An is just An=(1,1/n), and so intersection of all such is the limit on n, which would approach empty set.

Martinez39:
Expect if your "r" meant something else or I didn't get the context of the problem. I am sure that the infinite series Σ (1/r²) converges to π²/6 ie. Σ (1/r²) = π²/6.

Its not a regular sum.

Darivie04:

Its not a regular sum.

Okay.