Grumthorn starts an argument or two

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Jinxo
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Post by Jinxo » 14 Nov 2006 19:02

I prefer lollipops to Maths tbh

Far more useful
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Post by Jora » 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.
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Post by Grumthorn » 14 Nov 2006 19:03

Stormwern wrote:
Grumthorn wrote:
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?
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.

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.
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!
But I'm not using x, I'm using the limit, which is well defined, a number and in the case in point =1.
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Post by Grumthorn » 14 Nov 2006 19:05

Jinxo wrote:I prefer lollipops to Maths tbh

Far more useful
you try designing a space shuttle using lollipops.

Wheels would come off 1/2 way down the runway and all that sugar would never survive re-entry into the atmosphere.
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Post by Stormwern » 14 Nov 2006 19:07

x=1??? read again
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Post by Jora » 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...).
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Post by Stormwern » 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.
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Post by Fangfury » 14 Nov 2006 19:28

Must bookmark this post, it'll be very useful to come back to when I am having difficulty sleeping. :wink:
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Post by Stormwern » 14 Nov 2006 19:32

Lol, you brute :)
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Post by Grumthorn » 14 Nov 2006 19:43

Stormwern 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.
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 numbers

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)
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Post by Stormwern » 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.
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Post by Jora » 14 Nov 2006 20:06

We understand you, but the limit is defined as a number.
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Post by Stormwern » 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.
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Post by Jora » 14 Nov 2006 20:26

The limit is the number that the sequence approaches when the variable goes towards infinity.
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Post by Yiggie » 14 Nov 2006 21:08

Jora wrote:The limit is the number that the sequence approaches when the variable goes towards infinity.
Doesn't have to be infinity, could be any point where the function is 'defined', just has to get 'infinitely close' to that point.

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