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0 to infinity...???


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#1 Tim_Lou

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Posted 14 April 2004 - 05:16 PM

0 and infinity are actually mathematical meaningless numbers.

here are some of the problems about them.
1/0 =+infinity and -infinty, since in the graph y=1/x, y can be + and - infinity when x is zero.

hmm, what about 0/0 ??? is it infinity since its something over zreo? or 1 since they are the same.....or zero?? well actually, it can be any number since 0 times anything =0.

+-1/infinty=0, it comes from the graph y=1/x. what does 0*infinty equal?
0=+-1/infinty, +-(1/infinty)*infinty=1?? or zero since 0 times anything= 0.....in the graph y=0x, y is zero no matter what...but consider this graph y=infinty x. a line that has infinty slope, which is the y-axis. well when x is zero, it can be any point in the graph!!! so, infinty*0 can really equal anything!??

lim n--> infinity (n+1)/n=1. but what about lim n--> infinity [(n+1)/n]^n, this equals to "e" but not 1...??? isnt it that 1 to the whatever power=1??

hmm... zero and infinity, confusing and meaningless numbers.

plz reply if you got any idea, thx for anyone who replies. ;-)

#2 sanctus

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Posted 16 April 2004 - 03:19 AM

Originally posted by: Tim_Lou





1/0 =+infinity and -infinty, since in the graph y=1/x, y can be + and - infinity when x is zero.


I don't se any problem there it just a matter if you are approaching from the right or the left, it may help you if you remember that the real numbers arre dense, that means that if you got a (for example a positive one) number r arbitrarily close to 0, 1/r is arbitrarily big, but because R is dense you know that you can find an r' which is0<r'<r for any arbitrary small r and if you repeat this many times you find an r' whose inverse is arbitrarily bigger then the 1/r which you found before. You start off with r = 1 and then r= 2 and so on, so you will be able to imagine what infinity is like.

Originally posted by: Tim_Lou

hmm, what about 0/0 ??? is it infinity since its something over zreo? or 1 since they are the same.....or zero?? well actually, it can be any number since 0 times anything =0.


Well you found the answer...


Originally posted by: Tim_Lou

lim n--> infinity (n+1)/n=1. but what about lim n--> infinity [(n+1)/n]^n, this equals to "e" but not 1...??? isnt it that 1 to the whatever power=1??.


No, there is a thm that states that you can just put the limit inside, it's not 1 to power of n, because the variation due to the power is more important tham the one by the division.

Originally posted by: Tim_Lou

hmm... zero and infinity, confusing and meaningless numbers.


Confusing yes, meaningless no. It's very easy to find a meaning, if you haven't got an apple then you have 0 apple, if you happen to have a molecule of an apple then you have an arbitrary small quantity of an apple (nature is not dense:-) ). To imagine infinity take a conductor, it is a conductor until you apply not more than a certain electrical field, when this critical field is quite high we say there is an infinite supply of electrons, even if we know that there is not a infinite number.
Another way to imagine infinity is: close you're eyes, imagine a white empty space (like in matrix for example) and now you imagine a red line of infinite length, th farther you try to look to your left the line goes always on, same to the rifgt.

#3 Tim_Lou

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Posted 16 April 2004 - 04:02 PM

hmm, what about 0*infinty? this troubles me. does it equal to anything?

#4 bluetroutdoorknob

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Posted 16 April 2004 - 06:36 PM

i just came on the site to talk about zero and infinity and its crazy that it just happened to be on here. i was talking to my friend about how infinity divided by infinity equals infinity. he said it equaled one because any number over it self is equal to one. i said that infinity and zero aren't number, they represent nonexistence and existence respectively. because nonexistence is infinite and zero is finite.

i was trying to explain why infinity divided by infinity equaled infinity by talking about eternity. i told him that in eternity its eventually gonna come up that theres a class room filled with ted carters(his name) and the amount of time that would take is infinitely smaller to infinite do to the nature of eternity. so do to the amount of repeats of events this classroom full of ted carters would come about infinite times.
so in eternity there would be infinite class rooms full of ted carters. now if infinity is equal to infinity; and infinity divided by infinity is one. then this class room would exist constantly. i understand that this class room may exist infinite times but i highly doubt that it always has and always will exist at all points in time.
he said that this class room wouldn't exist in the first place because the chances of a whole class room full of teds was to close to zero. which as i wish everybody knew, time is of no factor in eternity.

now to the question of 0*infinity, i'll give you the same anwer my friend gave to me when i thought about it a few months ago. "**** you"

#5 Tim_Lou

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Posted 16 April 2004 - 07:21 PM

hmmm, good questions.

i think that infinity/infinty equals to everything.

in graph x/infinity, it is always zero (even infinity).... in the graph infinity/x, it is always +or-infinity (also when x is infinity)....

+-infinty=1/0 as we know (since 1/0=+- infinity)

+-infinity=1/0*0/1 (same as 0*infinity lol)
which comes out to be 0/0!!!!!!!

which can be anything. Meaningful, meaningless or any numbers(msut be positive and non-imaginary)...

hmm, i found out that many things involving w/ infinty and 0 equals to anything....
consider this, infinity/infinity=x
infinity x=infinity... x can really be anything (msut be positive and non-imaginary)!!!!

hmmm, +or-(infinity/infinity) = 0/0 = 0*infinity......???
wait, infinity/infinity has to be positive....so, +- is added.

(sry for not considering positive and negative, 1/0=+-infinity i forgot....)
(whats the point of cursing??????!!!!!????)

#6 sanctus

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Posted 19 April 2004 - 08:22 AM

Tim- Lou: "what about 0*infinity?"

It could be anything you want it to be (so it is not denified), this follows from:

x*y=z this implies that
a) y=z/x
B) x=z/y


Now, set x=0 and y any real number (finite!): you get always as a result z=0, but a) gives you 0/0 = y and B) gives you 0/y=0.

From the answer a) you see that 0/0 gives whatever you want, from the answer B) you see something which is intuitive (if you you divide 0 apples between 10 people everybody gets 0 apples) but a convention!

Now, set x=0 and y= infinity and assume that the result is z (a real number)
a) implies that infinity is z/0 which seems ok
B) implies that 0 is z/infinity which seems ok as well
I wrote seems ok, because in fact it isn't ok, because it works with any z you take.

I hope I was clear

#7 Tim_Lou

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Posted 19 April 2004 - 01:16 PM

and remember, 1/0=+or- infinity.
thats what i missed b4.
anyway, we seem to have the same answers! : )