Korean Job Discussion Forums

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"On the way"

[doggyji]

x = 0.99999999999.... (1)

10x = 9.99999999...... (2)

(2) - (1): 9x = 9

x=1

This is what I learned in middle school. I thought by inspection this is quite inarguable back then but it looks a bit lame because we might be dealing with a brand new imaginary number with a vague definition of limit and we are just applying the multiplication by 10 like we do in normal algebra.

According to the definition of limit, lim {An} = A when, for any number e > 0, there exists a natural number N <= n, which satisfies |An - A| < e.

Let's think about a series {An}=<0.9, 0.99, 0.999, 0.9999,...>
Then, lim An = 1 satisfying the condition and the nth element in this series can be expressed by 1 - 1/10^n where n is a natural number. For example, for 0.99, n is 2. Then does 0.9999...... belong to this series?

0.99999... = 1 - 1/10^n

We cannot pick one natural number n for this. Thus we have to say n doesn't exist for 0.9999.... In other words, 0.9999..... doesn't belong to the series {An}...! Then if 0.99999... has a status as a 'number,' lim An = 0.9999.... should be correct. But we don't say so. Here we get a hint on how 0.9999.... is 'defined' as lim An which is equal to 1. I'm not too confident if this sounds all very logical though.

I think there was some story about a Greek philosopher's logic. Maybe it was about a rabbit that can never catch up a turtle who started first in a race.. The concept of limit is so appealing...

[jacl]

[splok]

[doggyji]

[The Bobster]

This is not really basic addition, but rather some pretty high-end throretical math ... you knew that, right?

[out of context]

[Kwangjuchicken]

I just can't imagine anyone getting so serious about numbers.

[Hollywoodaction]

[shortskirt_longjacket]

1/3 represented as a decimal is in fact exactly equal to .3333333(repeating).

Think of it this way, people: The Romanization of certain Korean characters is not exact; it's approximate. But because you are converting one kind of thing to another, you have to assume that it's as close as you'll get. Kangnam? Gangnam? Which is it? Actually, it's both. And it's neither. And it's somewhere in between. The point is: we all agree that "G" or "K" can represent the first letter in the Korean alphabet.

Same with a decimal number being represented for a fractional number.

.33333333333333333333(repeating into infinity) is the same thing as 1/3. There is no other way to express it.

So, .333333333333333333 (repeating forever) + .666666666666666666 (repeating forever) = 1. Period. Full Stop. Whatever you say in your own dialect. The concept is the same. It's the same as 1/3 + 2/3 = 1. We're just saying it in a different language.

Seriously, this argument is like fighting over Kangnam vs. Gangnam. Same same!! There just isn't a "perfect" way to translate the Korean into English, so we all agree to recognize different systems as the same exact thing.

Let the argument end here.

[laogaiguk]

A little off topic here, but this is a problem in computer science.

Memory is finite, so when you divide numbers that end up being infinite, at some point you have to finally round it up (or truncate it). This has caused many problems. One was the Arianne 5 rocket in Europe Crashed into a small town if I remember right after veering offcourse. This is also a major problem for programmers programming for precision instuments, like any machine that doses people with radiation for cancer.

[The Cube]

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