Posted: 14 Nov 2006 19:02
I prefer lollipops to Maths tbh
Far more useful
Far more useful
Page 3 of 4
Posted: 14 Nov 2006 19:03
Given that even rational numbers have to be represented with period notation, I'd say that we actually imply a limit here, so 0.9999... means the limit and not the sequence.
Posted: 14 Nov 2006 19:03
But I'm not using x, I'm using the limit, which is well defined, a number and in the case in point =1.Stormwern wrote:Yes, it IS!! 0, but x is not infinity. Lim(x>oo) is the limit that is applied to the function 1/x. Don't confuse the terms!Grumthorn wrote:No the fact that the equals is valid _does_ entirely imply that the limit is a number. If I write (in a mathematical context) x = y it implies that x is a number, y is a number and that they are the same number.Stormwern wrote:Yes the = are valid, but that doesn't mean that the limit is a number. There is no number you can put instead of x to make 1/x=0.
In any case, I just gave you a function that has different answers for x=1 and x=0.9999.., isn't that enough?
Lim(x>oo) (1/x) is not arbitrarily close to 0, it does not 'approach 0' it _is_ 0. Without this fact you cannot do calculus, at all.
Posted: 14 Nov 2006 19:05
you try designing a space shuttle using lollipops.Jinxo wrote:I prefer lollipops to Maths tbh
Far more useful
Wheels would come off 1/2 way down the runway and all that sugar would never survive re-entry into the atmosphere.
Posted: 14 Nov 2006 19:07
x=1??? read again
Posted: 14 Nov 2006 19:11
Not x=1, but the limit=1, and what we write down there actually is the limit.
Now that I think about it, there are 2 representations for all non periodic numbers and only 1 for the others.
There is exactly one periodic representation for every rational number in our decimal notation (if you assume equality of 0.9... and 0.99...).
Now that I think about it, there are 2 representations for all non periodic numbers and only 1 for the others.
There is exactly one periodic representation for every rational number in our decimal notation (if you assume equality of 0.9... and 0.99...).
Posted: 14 Nov 2006 19:21
No, the limit is not equal to it's corresponding number, that's the whole point of a limit, to be "for our current intents and purposes equal", but not actually equal.
I would guess that there's an implied limit calculation in the infinite sum.
I would guess that there's an implied limit calculation in the infinite sum.
Posted: 14 Nov 2006 19:28
Must bookmark this post, it'll be very useful to come back to when I am having difficulty sleeping. 
Posted: 14 Nov 2006 19:32
Lol, you brute 
Posted: 14 Nov 2006 19:43
Your understanding of what a limit is is incorrect. Limits are not some fuzzy approximation of an iterative process. They are in and of themselves numbersStormwern wrote:No, the limit is not equal to it's corresponding number, that's the whole point of a limit, to be "for our current intents and purposes equal", but not actually equal.
I would guess that there's an implied limit calculation in the infinite sum.
http://mathworld.wolfram.com/Limit.html
http://en.wikipedia.org/wiki/Limit_%28mathematics%29
The 'Limit of a function at infinity' section in the wiki may help you clear up your confusion between f(x) and lim f(x)
Posted: 14 Nov 2006 20:03
It seems infact we are talking about two different things, read the first post I made on page 2 and I think you'll see what I mean.
Posted: 14 Nov 2006 20:06
We understand you, but the limit is defined as a number.
Posted: 14 Nov 2006 20:22
Seems it was me getting the terms mixed up, sorry, the limit is the function value? I'm talking about the variable.
Posted: 14 Nov 2006 20:26
The limit is the number that the sequence approaches when the variable goes towards infinity.
Posted: 14 Nov 2006 21:08
Doesn't have to be infinity, could be any point where the function is 'defined', just has to get 'infinitely close' to that point.Jora wrote:The limit is the number that the sequence approaches when the variable goes towards infinity.
P.S. jk, that last quote isn't real :> sue meJora wrote:No one likes a smart ass, Yiggie!.