what is a singularity?

Discussion of theories involving time as a dimension, time travel, relativity, branes, and so on, usually applying to the "real" universe which we live in.

what is a singularity?

Postby solodeath » Sun Mar 13, 2005 7:21 pm

what is the meaning of singularity in our 3D space and time? how dose it link with our world? what is the idea of this meaning of this word? where did this world come from?
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Postby jinydu » Sun Mar 13, 2005 8:22 pm

Well, the word singularity can have different meanings in different areas. For instance, in complex analysis, a singularity is a point where a function does not have a derivative.

But in your context, I think you're thinking about a singularity in terms of physics. What you probably have in mind is a point in spacetime with zero volume and infinite density.
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Postby solodeath » Sun Mar 13, 2005 8:58 pm

if something have 0 volume then dose it mean it have 0 area? then if it is a point which have no area then is it a point at all? i mean in a 3D world?

If it have infinite density, then what dose that say about its mass?
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Postby jinydu » Sun Mar 13, 2005 9:48 pm

solodeath wrote:if something have 0 volume then dose it mean it have 0 area?


If you mean 0 surface area, then yes.

solodeath wrote:then if it is a point which have no area then is it a point at all? i mean in a 3D world?


Of course! When was the last time you saw a point that did have a surface area?

solodeath wrote:If it have infinite density, then what dose that say about its mass?


Density = Mass/Volume

which implies that

Mass = Volume * Density

But volume is zero and density is infinite. Since 0*infinity is indeterminate, it doesn't say anything about the mass.
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Postby solodeath » Sun Mar 13, 2005 11:30 pm

Mass = Volume * Density
Mass = 0 * infinite
let infinite be X
X ---> a value that is so big that nothing is bigger then it.
let 0 be nothing
so , nothing * x
it is = nothing * value that is so big that nothing is bigger then it
now, in math senth lets say if something cost infinite amount of and u bought 0 of them then how much did u spent? well itz 0.
now if we use the same logic and say the same same then
Mass = 0

If mass = 0 then how mould it be anything? last time i chacked i thought we call it "nothing".
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Postby houserichichi » Sun Mar 13, 2005 11:42 pm

That's a cute little analogy with the money spent, but when you deal with infinity in math you actually need to bring in calculus which will then tell you that "zero times infinity" is indeterminate (doesn't have an answer).
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Postby solodeath » Mon Mar 14, 2005 12:27 am

but even lest say
lim X --->infinite
where there is no right lim
and let lim Y----> 0
then X*Y = indeterminate....
how????
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Postby houserichichi » Mon Mar 14, 2005 3:48 am

The easiest answer is that infinity isn't a number. Values tend towards it but never get there so the "normal" rules of arithmetic don't apply. Also, by straight arithmetic you can transform 0 times infinity into

0/(1/infinity) (indeterminate)

and also

infinity/(1/0) (indeterminate again). Did that help?
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Postby jinydu » Mon Mar 14, 2005 6:43 am

Suppose X = 1/n and Y = n. What is the limit as n goes to infinity of X * Y?

Now, what happens if X = 2/n and Y = n and you take the limit?

And what if X = a/n and Y = n, where a is some fixed constant?

As you can see, the value of "0 * infinity" depends on how the pair of numbers approach 0 and infinity. That's why its called indeterminate. By contrast, 1 * 1 is not indeterminate, because if a --> 1 and b --> 1, then a*b approaches the same value, irrespective of any further details.
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Postby solodeath » Mon Mar 14, 2005 9:34 pm

i dont understand...
where is ur "let" statment?
what do u mean by X, Y, n, a?
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Postby houserichichi » Tue Mar 15, 2005 1:29 am

What Jinydu's post meant in words is the following:

If we let n be any number (we'll say any real number for sake of simplicity) and define the number X as its reciprocal and say that Y is just renaming the number n then, for example if n=2 then X = 1/2 and Y = 2. Right? The first question posed:

What is the limit as n goes to infinity of X * Y?


is precalc and is asking what is the limit of X times Y (where X and Y are functions of n defined above) as n increases to infinity.

The second question:

Now, what happens if X = 2/n and Y = n and you take the limit?


redefines the function X by putting a 2 on the top and poses the question whether it makes a difference. Same logic goes for replacing that 2 with any constant (real for my explanation of it) number...does it change the limit any?

The overall point was summed together with the statement

the value of "0 * infinity" depends on how the pair of numbers approach 0 and infinity. That's why its called indeterminate


It's just precalc, but if you don't have that under your belt it won't make much sense. I can recommend some decent sources if you feel the urge to delve into it further. Infinity is mentioned often and discussed thoroughly in both calculus (analysis) and set theory.
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Postby solodeath » Tue Mar 15, 2005 3:48 am

yea.... u did not answer the question. see what i ask is the
"let" statement
u know, the let x be Volume.... and such on
caz math without meaning is just numbers
sorry if im so rude, but i just dont understand what is ur x?
mass?
density?
what is it?
there are no units....
thx for trying to answer
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Postby jinydu » Tue Mar 15, 2005 7:10 am

In this context, x is a shorthand way of saying "some number".
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Postby brasileiro » Sun May 08, 2005 3:58 am

Man I love these forums and discussions... :lol:
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