Eff this, philly mike is an idi0t, ask zdunklee.

[Philly Mike]

Okay this is spilling over from the arguments with friends topic, i figure i would move it here to get that on topic.

here is the beginning of the debate. http://fbhw.proboards47.com/index.cgi?bo...252&page=1

continue on...

[zdunklee]

Way to open this can of worms mike...I totally blame you for this one.

[Allyson]

Ok I did some researching and popular belief agrees with zdunklee. I can't conform.

Couldn't this be considered similar to Zeno's dichotomy paradox? Where theoretically you will never reach that stationary object, just get infinitely close to it? Same thing. 0.999... comes infinitely close to 1, but it never is 1.

[zdunklee]

Zeno's dichotomy paradox doesn't even say that, it says you can't even begin to start towards the object. I guess you could kind of say that, but the mathematical definition of of real numbers is:

A cauchy sequences of rational numbers whose limit is X, where X is the real number in question, thus all real numbers are in fact limits of a sequence of rational numbers, which is why .9999... = 1.

A cauchy sequence is a sequence whose numbers become arbitrairly close to each other as the sequence progresses. Otherwise no matter what distance from 1 you want me to get .9999... to 1, I can always make it closer than that.

[Allyson]

Ok it goes both ways and I was thinking about it the other way. Even still, your way supports my point. I'm saying that {.....1/8, 1/4, 1/2, 1} is infinite, so matter how small it gets you can still take that half step. Every time you go to take that half step, you have to take half that half, and so on. That sequence will never start at 0, it will just be infinitely small.

[Allyson]

no matter what distance from 1 you want me to get .9999... to 1, I can always make it closer than that.

Exactly.

[Philly Mike]

with the kind of logic that .999... = 1 it would mean that .111... = .2

if that is the case then .999... could never actually be considered a number, and the same goes with any number that would go on as infinate.

oh and

Way to open this can of worms mike...I totally blame you for this one.

and well, what do you think this post was about

[zdunklee]

It is the same thing, just stated the other way, but that IS the definition of the real numbers, which is why .9999...= 1.

[Allyson]

.999... is real but it is irrational, meaning it could never be expressed as a fraction. 1 = 1/1.

[Philly Mike]

It is the same thing, just stated the other way, but that IS the definition of the real numbers, which is why .9999...= 1.

Thing is if .9999... = 1 and .1111...= .2 then that would mean .xxxx... doesn't even count as a number therefore there is no reason to show it as a quantity.

There is a reason this is represented as a decimal, and it isn't just to have a fancy way of saying the next number up.

[zdunklee]

.999... is real but it is irrational, meaning it could never be expressed as a fraction. 1 = 1/1.

By definiton 1 = the limit the sequence {1/1 + 1/1 + 1/1 + ...}

but it is also true that 1= the limit of the sequence {9/10 +99/100 +999/1000 + ...}

which again is using the definiton of the real numbers, thus both equal one by definiton.

[zdunklee]

It is the same thing, just stated the other way, but that IS the definition of the real numbers, which is why .9999...= 1.

Thing is if .9999... = 1 and .1111...= .2 then that would mean .xxxx... doesn't even count as a number therefore there is no reason to show it as a quantity.

There is a reason this is represented as a decimal, and it isn't just to have a fancy way of saying the next number up.

Sorry mike, I didn't mean .111.. = .2, that is not true at all, that reply was to allyson. How are you saying it isn't a number?

[Allyson]

1 = 1
{1/1 + 1/1 + 1/1 + ...} = {9/10 +99/100 +999/1000 + ...}
{1/1 - 9/10 + 1/1 - 99/100 + 1/1 - 999/1000 + ...} = 0
{1/10 + 1/10 + 1/1000 + ...} = 0?

[krystal]

Question: would 1.9999~ = 2?

[Queenie]

Question: would 1.9999~ = 2?

It would if you were rounding numbers.

[dingdongyo]

this seemed to help krystal understand:

let me ask you this: if 0.999... <> 1, what do you subtract from 1 to get 0.999...?

and

Question: would 1.9999~ = 2?

yes

----

x = 1.999...
10x = 19.999...

(10x - x) = (19.999... - 1.999...)

9x = 18

x = 2

[zdunklee]

1 = 1
{1/1 + 1/1 + 1/1 + ...} = {9/10 +99/100 +999/1000 + ...}
{1/1 - 9/10 + 1/1 - 99/100 + 1/1 - 999/1000 + ...} = 0
{1/10 + 1/10 + 1/1000 + ...} = 0?

Oops, I effed up my sequences... they aren't added they simply are

1 = lim {1,1,1,...} and 1= lim {0,9/10, 99/100, 999/1000,...) if you add them they get infinitly bigger...1+1+1+!... = infinity..sorry for the confusion there, I am an idiot for that one.

You can now however subtract the two correct sequences to get:

1 - 1 = 0
lim {1-0, 1-9/10, 1-99/10,...} = 0.

[Allyson]

1 = 1
{1/1 + 1/1 + 1/1 + ...} = {9/10 +99/100 +999/1000 + ...}
{1/1 - 9/10 + 1/1 - 99/100 + 1/1 - 999/1000 + ...} = 0
{1/10 + 1/10 + 1/1000 + ...} = 0?

Oops, I effed up my sequences... they aren't added they simply are

1 = lim {1,1,1,...} and 1= lim {0,9/10, 99/100, 999/1000,...) if you add them they get infinitly bigger...1+1+1+!... = infinity..sorry for the confusion there, I am an ambulance driver for that one.

You can now however subtract the two correct sequences to get:

1 - 1 = 0
lim {1-0, 1-9/10, 1-99/10,...} = 0.

I knew you miswrote I just couldn't figure out what you meant. I perfectly get what you're saying, I just don't agree with the rule that .999... = 1 because in my head it doesn't, it equals .999... It's kind of like identical twins. They are essentially the same, same genetic makeup and all, but they are not the same person.

[zdunklee]

You don't know how long it took me to believe that it was true. My last year of school when I took Real Analysis is when I finally believed it. In Real Analysis you start the class as if the real numbers don't even exist and have to prove they exist based only on the rational numbers...

Without 0.999... = 1 then it is impossible to construct the real numbers.

[Allyson]

Eh maybe if I started from the beginning I'd have an easier time. I avoided real analysis and I hate proofs, that's why I did statistics. I can actually use my major in practical ways. Wow.

[dingdongyo]

on another note, i can prove that the slower you work, the more money you make:

work = rate X time

time = money

work = rate x money

money = work/rate

as rate -> 0, money -> infinity

therefore, i screw around on a message board all day

[zdunklee]

Eh maybe if I started from the beginning I'd have an easier time. I avoided real analysis and I hate proofs, that's why I did statistics. I can actually use my major in practical ways. Wow.

Yea, my major is garbage, unless you want to debate math or teach at a college, and I don't want to have to get a phd....eff me.

[krystal]

on another note, i can prove that the slower you work, the more money you make:

work = rate X time

time = money

work = rate x money

money = work/rate

as rate -> 0, money -> infinity

therefore, i screw around on a message board all day

+1

[zdunklee]

on another note, i can prove that the slower you work, the more money you make:

work = rate X time

time = money

work = rate x money

money = work/rate

as rate -> 0, money -> infinity

therefore, i screw around on a message board all day

Ha, I can also prove women are evil:

Women takes time and money so,

Women = time x money

Time = money, thus

Women = money x money = money ^ 2

Money is the root of all evil

money = sqrt(evil)
=> money^2 = evil

since women = money^2

women = evil




note: I do not believe this proof, but I can still use it

[krystal]

on another note, i can prove that the slower you work, the more money you make:

work = rate X time

time = money

work = rate x money

money = work/rate

as rate -> 0, money -> infinity

therefore, i screw around on a message board all day

Ha, I can also prove women are evil:

Women takes time and money so,

Women = time x money

Time = money, thus

Women = money x money = money ^ 2

Money is the root of all evil

money = sqrt(evil)
=> money^2 = evil

since women = money^2

women = evil




note: I do not believe this proof, but I can still use it

Tell us something we don't know.

[-Jiggy-]

This thread makes me feel stupid!

[Queenie]

<<is with Jiggy on this.

<<not much on math . . . give me bookkeeping, i'll show ya

[Philly Mike]

this seemed to help krystal understand:

let me ask you this: if 0.999... <> 1, what do you subtract from 1 to get 0.999...?

This makes no sense. if you want to look at it like that
what do you subtract from 1 to get to 0.888...

and the point i was trying to make about the .999... may as well not be considered a number is because saying .999... = 1 is the same as saying .111... = .2 because it is just taking it up to the next number after the decimal.

[airhornahole]

From the discussion, some people would say that difference between 0.999.... and 1 is so small it can be ignored.

Let me ask this question.

If you had a $15 million boat, would you rather miss an iceberg by the difference between the two or by ignoring it, sink your boat?

It may be infinitesimally (sp?) small, but the difference is still there.

[speedbump]

From the discussion, some people would say that difference between 0.999.... and 1 is so small it can be ignored.

Let me ask this question.

If you had a $15 million boat, would you rather miss an iceberg by the difference between the two or by ignoring it, sink your boat?

It may be infinitesimally (sp?) small, but the difference is still there.

No there is no difference, that's kind of the point. .999... keeps going to infinity. If there is an unimaginably small distance between the boat and the iceberg, because that difference goes to infinity, there is a distance that is always smaller so at no point can you make a distinction between when the iceberg and boat are touching or when they are not. When you stop and acknowledge any distance between the boat and the iceberg, you aren't considering the fact that you are dealing with infinity.

[zdunklee]

From the discussion, some people would say that difference between 0.999.... and 1 is so small it can be ignored.

Let me ask this question.

If you had a $15 million boat, would you rather miss an iceberg by the difference between the two or by ignoring it, sink your boat?

It may be infinitesimally (sp?) small, but the difference is still there.

They are equal according to the DEFINITON of the real numbers, thus the distance between the two is 0.

[zdunklee]

this seemed to help krystal understand:

This makes no sense. if you want to look at it like that
what do you subtract from 1 to get to 0.888...

and the point i was trying to make about the .999... may as well not be considered a number is because saying .999... = 1 is the same as saying .111... = .2 because it is just taking it up to the next number after the decimal.

But .111.... is not equal to .2, the limit of .111... as it goes to infinity is 1/9, and the limit of .2 as it goes to infinity is 2/10 or 1/5.

[dingdongyo]

this seemed to help krystal understand:

This makes no sense. if you want to look at it like that
what do you subtract from 1 to get to 0.888...

and the point i was trying to make about the .999... may as well not be considered a number is because saying .999... = 1 is the same as saying .111... = .2 because it is just taking it up to the next number after the decimal.

it upsets me that you missed the point of my example, but you've already been addressed.

i liked my example....

[taekahn]

Well put, and here i thought i was going to have to defend my position. But since i went through the drastic effort to get here, i might as well as throw a straw in here.
Mike, there is a number between .111

[motorboatking]

1=1
.999..... doesn 't have a specific value. Yet it's infinitely less than 1.

[zdunklee]

1=1
.999..... doesn 't have a specific value. Yet it's infinitely less than 1.

Yes it does, just like 1/2 = 2/4 = 4/8, etc 0.999... = 1, they are the same number based on the DEFINITON of the real numbers, I don't get how that is hard to understand, there is only one definition for real numbers...

As found on a math site:

In the last few decades, researchers of mathematics education have studied the reception of this equality among students, many of whom initially question or reject this equality. Many are persuaded by textbooks, teachers and arithmetic reasoning as below to accept that the two are equal. However, they are often uneasy enough that they offer further justification. The students' reasoning for denying or affirming the equality is typically based on one of a few common erroneous intuitions about the real numbers; for example that each real number has a unique decimal expansion, that nonzero infinitesimal real numbers should exist, or that the expansion of 0.999

[Philly Mike]

This makes no sense. if you want to look at it like that
what do you subtract from 1 to get to 0.888...

and the point i was trying to make about the .999... may as well not be considered a number is because saying .999... = 1 is the same as saying .111... = .2 because it is just taking it up to the next number after the decimal.

But .111.... is not equal to .2, the limit of .111... as it goes to infinity is 1/9, and the limit of .2 as it goes to infinity is 2/10 or 1/5.

[quote="taekahn"]Well put, and here i thought i was going to have to defend my position. But since i went through the drastic effort to get here, i might as well as throw a straw in here.
Mike, there is a number between .111

[Rock Monster]

I've been trying to stay away from this argument, but I can not anymore.

You can't compare the numbers 1 and .9999......

One is a rational # (1) and one is irrational (.99999)

It's like comparing an apple to a drawing of an apple.

[zdunklee]

Yes, but 1 represents the same REAL number that 0.999... represents. Rationals and irrationals make up the real numbers, but when comparing them as strictly real numbers rational and irrational do not matter as they are simply seperate subsets of the reals.

Here is a good example of what would happen if this was not true:

Although the real numbers form an extremely useful number system, the decision to interpret the notation "0.999

[motorboatking]

x = 0.999...
5x = 4.999...5
5x-x = 4.999...5 - 0.999...
4x = 3.999...6
/4 /4
x= 0.999...
:o