Theories of the universe

DavidMarq said:
But what if like in this process we are dividing infinity by a finite number an infinite amount of times.

/head explodes :eek:
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so your dividing infinaty by a finate number times an infinate number.

so you have I/(I*F)

I*F = I

so you have I/I = 1
 
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yantorsen said:
so your dividing infinaty by a finate number times an infinate number.

so you have I/(I*F)

I*F = I

so you have I*I = 1
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But going back to the first cut.

You said

∞/2=∞

Giving 2 ribbons length ∞

Repeat the cut to each ribbon and we have 4 ribbons of length ∞

Repeat the cut ∞ number of times we have ∞ ribbons of length ∞

Or do we not?

/head explodes again ;)
 
DavidMarq said:
But going back to the first cut.

You said

∞/2=∞

Giving 2 ribbons length ∞

Repeat the cut to each ribbon and we have 4 ribbons of length ∞

Repeat the cut ∞ number of times we have ∞ ribbons of length ∞

Or do we not?

/head explodes again ;)
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no, because your looking at infinty as just a very big number, not an eternal number.

if you divided infinty by 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 you would still have infinty.

but by dividing by infinity you always get 1.

dividing anything by itself always = 1.
 
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yantorsen said:
no, because your looking at infinty as just a very big number, not an eternal number.

if you divided infinty by 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 you would still have infinty.

but by dividing by infinity you always get 1.

dividing anything by itself always = 1.
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There are an infinite amount of natural numbers.
There are an infinite amount of real numbers.

Divide one by the other and the answer most certainly is not 1!
 
Conscript said:
in.gif
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there is 1 major flaw with your theory.

first of all if you cut the ribbon into 2 you are at the beginning of the 2, the beginning can now also be classed at the end. if you take these 2 end pieces you can cut along them and you wont be creating new infinite pieces, you will be creating finite piece.


-------------------------------snip---------------------------
--------------snip-------------snip---------------------------

see what Im getting at?

my point is as you cant divide infinity you cant really use it in such an example.
 
DavidMarq said:
But going back to the first cut.

You said

∞/2=∞

Giving 2 ribbons length ∞

Repeat the cut to each ribbon and we have 4 ribbons of length ∞

Repeat the cut ∞ number of times we have ∞ ribbons of length ∞

Or do we not?
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You have to define (at least in a theoretical sense) what you mean by an infinite ribbon (and what you mean by a cut).

I'd say the most "natural" definition would be to model the ribbon as the real line, and a cut at 'x' means splitting into the sets {y:y<x} and {y:y>x}. In which case after n cuts you end up with n-1 finite pieces and 2 infinite ones.

But you could model an infinite ribbon using the "long real line" (using the same definition of cutting at 'x'), in which case it's perfectly possible to divide it into an infinite number of parts of infinite length. (Using what I think is a perfectly reasonable definition of 'length' over the long reals, though your mileage may vary).

Edit: (Actually, I think you might need the "long long real line" to make the last example work. Not sure).
 
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Haircut said:
Natural numbers are 1,2,3,...
Basically whole numbers greater than 0

Real numbers are anything that can be expressed as a decimal.
For instance pi is a real number, but not a natural number.
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well it makes no difference then, two numbers that are the same divided by each other will always equal 1.


and also you can't actually divide infinity by two because it has no centre point.
 
yantorsen said:
well it makes no difference then, two numbers that are the same divided by each other will always equal 1.


and also you can't actually divide infinity by two because it has no centre point.
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Oh I completely agree, but that's an entirely different statement to saying "infinity divided by itself is always 1."

I don't wish to be patronising, but if you don't know what what natural and real numbers are you aren't qualified to make that statement
 
yantorsen said:
no, because your looking at infinty as just a very big number, not an eternal number.

if you divided infinty by 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 you would still have infinty.

but by dividing by infinity you always get 1.

dividing anything by itself always = 1.
Click to expand...

I am doing ∞ sequential iterations of the first cut.

Where in this sequence of iterations does ∞/2=∞ no longer hold true?
 
Haircut said:
Oh I completely agree, but that's an entirely different statement to saying "infinity divided by itself is always 1."

I don't wish to be patronising, but if you don't know what what natural and real numbers are you aren't qualified to make that statement
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Well it's only a case of logic, knowing what real and natural numbers are is a case of knowledge not logic, having not even finished my maths GCSE yet I wouldn't have learnt about them yet, but I can sill have logic.
 
yantorsen said:
Well it's only a case of logic, knowing what real and natural numbers are is a case of knowledge not logic, having not even finished my maths GCSE yet I wouldn't have learnt about them yet, but I can sill have logic.
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Well if you get as far as doing a maths degree look back to this thread once you've completed your real analysis modules!

Infinity isn't a number, logical or not what you have posted is incorrect.
 
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