Need MATH help (set theory)

[JJChicken]

Just want to ask if the following two expressions are equivalent (where U=Union of sets, I= intersection of sets and "from a=c to infinity" means putting a=c as a subscript on U (or I) and infinity as a superscript and f(n) is a function of n)

* (from N=1 to infinity) U [(from n=N to infinity) I f(n)]

* I (from n=1 to infinity) f(n)


THANKS

 

[JJChicken]

bunmp

 

[sao123]

im going to start by guessing no...
based on:

IF f(N=n) <= 0 for any 1 >= N >= Infinity

then

N U I(F(n)) does not equal I(F(n))

 

[JJChicken]

Originally posted by: sao123
im going to start by guessing no...
based on:

IF f(N=n) <= 0 for any 1 >= N >= Infinity

then

N U I(F(n)) does not equal I(F(n))

sorry can you explain. By the way, in the original question which I adapted for this post, think of f(n) as a set of sequences (e.g. 011100..., 01010101.... etc)

 

[drdops]

3

 

[JJChicken]

bump

 

[sao123]

Originally posted by: Barack Obama

Originally posted by: sao123
im going to start by guessing no...
based on:

IF f(N=n) <= 0 for any 1 >= N >= Infinity

then

N U I(F(n)) does not equal I(F(n))

sorry can you explain. By the way, in the original question which I adapted for this post, think of f(n) as a set of sequences (e.g. 011100..., 01010101.... etc)

ignore what i was saying... I had my U and I mixed up.

 

[JJChicken]

Originally posted by: sao123

Originally posted by: Barack Obama

Originally posted by: sao123
im going to start by guessing no...
based on:

IF f(N=n) <= 0 for any 1 >= N >= Infinity

then

N U I(F(n)) does not equal I(F(n))

sorry can you explain. By the way, in the original question which I adapted for this post, think of f(n) as a set of sequences (e.g. 011100..., 01010101.... etc)

ignore what i was saying... I had my U and I mixed up.

oh okay. bump!

 

[Necrosaro420]

You will never need any of this in real life unless your planing on being a scientist.

 

[JJChicken]

Originally posted by: Necrosaro420
You will never need any of this in real life unless your planing on being a scientist.

That's true, although I will need this in my (hopeful) future career (derivative pricing).

 

[JJChicken]

Paging Dr. Pizza...

 

[DrPizza]

You've got me.. I tried to locate some resources online, but couldn't find anything that would help me understand completely what you were saying. I hadn't run into anything like that in my coursework, at least, not t hat I recall.

 

[MSCoder610]

For a specific n, is f(n) a set of multiple values? I can't quite follow what you meant by "think of f(n) as a set of sequences (e.g. 011100..., 01010101)"

 

[sao123]

Originally posted by: Barack Obama
Just want to ask if the following two expressions are equivalent (where U=Union of sets, I= intersection of sets and "from a=c to infinity" means putting a=c as a subscript on U (or I) and infinity as a superscript and f(n) is a function of n)

* (from N=1 to infinity) U [(from n=N to infinity) I f(n)]

* I (from n=1 to infinity) f(n)


THANKS

lets see if I can try this again...

The union of 2 sets... n U I[F(n)] is larger than either of the single sets S=n or S=I[F(n)]

UNLESS, one set (n) is exclusively a subset of the other set I[F(n)]


Example:

Given the Set
S[ n ] = {0,1,2} and F(n) = n1 * n2
then 0*0 = 0, 0*1 = 0, 0*2 = 0, 1*1 = 1, 1*2 = 2, 2*2 = 4
S[ F(n) ] = {0,1,2,4}
{0,1,2} U {0,1,2,4} = {0,1,2,4}... n U I[F(n)] = I[F(n)] is true


S[ n ] = {2,3,4} and F(n) = n1 * n2
then 2*2 = 4, 2*3 = 6, 2*4 = 8, 3*3 = 9, 3*4 = 12, 4*4 = 16
S[ F(n) ] = {4,6,8,9,12,16}
{2,3,4} U {4,6,8,9,12,16} = {2,3,4,6,8,9,12,16} ... n U I[F(n)] = I[F(n)] is false