If you add together an infinite number of infinitely small numbers?

[mephiston5]

If you add together an infinite number of infinitely small numbers (being greater then 0 but just barely) what size number would you get?

Just wondering what everyone thought around here, I am thinking it would more or less = 0 if you round it to the nearest whole number.

I am asking because one of my finance classes had a lecture on the "correct" way to value stocks, stating that the value of a stock is = to the value of the infinite stream of said stock?s future dividends, discounted back into today?s dollars.

 

[tfinch2]

The correct answer would be infinity, but realistically it'd be close to zero.

 

[Soccerman06]

are you asking infinity x 1/infinity?

beause in calculus, that would be infinity.

 

[So]

actually, I believe the limit would be undefined. infinity / infinity is non computable and l'hospital's rule (SP?) would be required to compute the defining function, but assuming:

lim (x -> infinity) of x * 1 / x = 1

 

[Phlargo]

infinity. adding any numbers infinitely will result in infinity

 

[markgm]

Originally posted by: Phlargo
infinity. adding any numbers infinitely will result in infinity

What he said.

 

[Rubycon]

41.999999 does not equal 42.

 

[tfinch2]

Originally posted by: MS Dawn
41.999999 does not equal 42.

O RLY?

 

[UncleWai]

Originally posted by: MS Dawn
41.999999 does not equal 42.

NO WAI!

 

[SamurAchzar]

Actually, I think the original question can be answered by looking at the history of my bank account. I'll tell you one thing - The resulting number is not significant.

 

[DVK916]

Originally posted by: Phlargo
infinity. adding any numbers infinitely will result in infinity

Adding 0 an infinite number of times is still 0.

 

[So]

Originally posted by: DVK916

Originally posted by: Phlargo
infinity. adding any numbers infinitely will result in infinity

Adding 0 an infinite number of times is still 0.

dx is only ~= 0 not == 0

 

[PlatinumGold]

Originally posted by: mephiston5
If you add together an infinite number of infinitely small numbers (being greater then 0 but just barely) what size number would you get?

Just wondering what everyone thought around here, I am thinking it would more or less = 0 if you round it to the nearest whole number.

I am asking because one of my finance classes had a lecture on the "correct" way to value stocks, stating that the value of a stock is = to the value of the infinite stream of said stock?s future dividends, discounted back into today?s dollars.

adding up an infinite number of numbers < 0 = 1, right?

 

[So]

Originally posted by: PlatinumGold

Originally posted by: mephiston5
If you add together an infinite number of infinitely small numbers (being greater then 0 but just barely) what size number would you get?

Just wondering what everyone thought around here, I am thinking it would more or less = 0 if you round it to the nearest whole number.

I am asking because one of my finance classes had a lecture on the "correct" way to value stocks, stating that the value of a stock is = to the value of the infinite stream of said stock?s future dividends, discounted back into today?s dollars.

adding up an infinite number of numbers < 0 = 1, right?

See my post above.

 

[GuitarDaddy]

3.142835--------------------------------

I like pie!

or maybe a smidgion

 

[mephiston5]

Yeah, it is an odd question. But since I brought it up the finance people use this equation to value stocks

P = D1/(1+Rs)^1 + D2/(1+Rs)^2 + .......... + DX/(1+Rs)^X

So as you can see, the first 10 or so years mean a whole lot more then the next 1000 years, and in the end you are adding an infinite number of infinitely small numbers.

value of stock = P
Value of the Dividend = D
Required rate of return at a given level of risk = Rs

However, they do not really use that equation; it can be simplified down into

P = D1/Rs-G

For special theoretical cases where G = the firm?s growth each year and it is constant from year to year, which of course is not realistic, but with out it, they would not be able to put it on the test?.

 

[SophalotJack]

69?

Sorry was thinking about the 3 Jessicas.

 

[So]

Originally posted by: tfinch2

Originally posted by: MS Dawn
41.999999 does not equal 42.

O RLY?

No, but

41.999... definitely DOES equal 42.

 

[Midlander]

Originally posted by: GuitarDaddy
3.142835--------------------------------

I like pie!

or maybe a smidgion

3.14159265...

 

[chuckywang]

Originally posted by: mephiston5
If you add together an infinite number of infinitely small numbers (being greater then 0 but just barely) what size number would you get?

Just wondering what everyone thought around here, I am thinking it would more or less = 0 if you round it to the nearest whole number.

I am asking because one of my finance classes had a lecture on the "correct" way to value stocks, stating that the value of a stock is = to the value of the infinite stream of said stock?s future dividends, discounted back into today?s dollars.

You need to be more specific.

 

[dxkj]

Originally posted by: mephiston5
If you add together an infinite number of infinitely small numbers (being greater then 0 but just barely) what size number would you get?

Just wondering what everyone thought around here, I am thinking it would more or less = 0 if you round it to the nearest whole number.

I am asking because one of my finance classes had a lecture on the "correct" way to value stocks, stating that the value of a stock is = to the value of the infinite stream of said stock?s future dividends, discounted back into today?s dollars.

The answer is ~ 1

 

[dxkj]

Originally posted by: markgm

Originally posted by: Phlargo
infinity. adding any numbers infinitely will result in infinity

What he said.

but the numbers are infinitely small, so its a stalemate.

 

[UncleWai]

Ok, I just look at your question. What you want to read about is geometric series.

The dividends in PV is shrinking and approaching zero as n becomes inifinity.

I think your title is too vague. You cannot really express a really small infinite number. Your answer changes depend on how you define the inifinitely small numbers, no?

 

[Howard]

sum from i = 0 to infinity of limit of x as x approaches 0?

 

[Rock Hydra]

I hate numbers, there's like too many of them and stuff