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

[Rock Monster]

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.

An apple and an orange are both seperate fruits. Can an Orange represent the same fruit as an apple?

[zdunklee]

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

Not true, 5(0.999...) = 4.99999... = 5 there is no 5 at then end because there is no end.

[taekahn]

Mike, if you subtract .111

[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.

An apple and an orange are both seperate fruits. Can an Orange represent the same fruit as an apple?

Now you are arguing nonsense, a subset has it's own seperate properties that are derived from the original set, but when compared in the original set they have additional properties that do not necessairly fit the subsets themselves. Rationals and Irrationals have NOTHING to do with the real numbers other than the fact that they are subsets of the real numbers.

Also, an apple and an orange are in fact SEPERATE fruits like you said, 0.999... and 1 are NOT seperate numbers.

[zdunklee]

How about everyone try this, take out your calculator and add 0.9999999 with as many decimal places as you want, and then add 0.1111111 with the same number of decimal places and tell me with it says. I bet it doesn't give you the number 1 as an answer (unless you simply pick 0.9 and 0.1).

[Rock Monster]

Now you are arguing nonsense, a subset has it's own seperate properties that are derived from the original set, but when compared in the original set they have additional properties that do not necessairly fit the subsets themselves.

apples and oranges has it's own seperate properties that are derived from the original fruit, but when compared in the original set (Fruit as a family) they have additional properties that do not necessairly fit the subsets (apples and oranges) themselves

Rationals and Irrationals have NOTHING to do with the real numbers other than the fact that they are subsets of the real numbers.

Apples and oranges have NOTHING to do with the fruits other than the fact that they are subsets of the fruits

My whole point is that they have nothing to do with each other, except being called numbers, therefore, can't be compared to each other.

[zdunklee]

What additional properties do ALL fruits have that apples and oranges don't have? I think you missed the point. The set of all Real Numbers has properties that neither the Irrational numbers or Rational numbers have (they have some, but not all properties of the reals).

[taekahn]

[quote author=zdunklee board=politics thread=3265 post=76383 time=1236798669]numbers ... can't be compared to each other.

Wow, i think we just broke mathmatics.

[zdunklee]

Haha, wow...sorry Rock, but I think that might be the biggest ambulance driver statement I have seen here.


Thanks for pointing that out, cause I didn't actually notice it... 8-)

[Rock Monster]

Ok, one last time... Irrational and rational. They are different. Like apples and oranges. You are failing to even admit that fact.


this is pointless.



I knew I should have never spoke up in this thread.

[zdunklee]

No, they are different SUBSETS, they are BOTH REAL NUMBERS, they are not necesaily representing different REAL NUMBERS. You really need to look up how irrationals and rationals are defined before arguing mathematics with a mathematician... :


Also, eff you all for making me actually use my degree...


Rock, to make it a little more clear Apples and Oranges are different Species in the same Family of fruits, Irrationals and Rationals are NOT different species of the same Family of numbers, they are all numbers. The difference between Irrational and Rational is irrevalant unless you are strictly dealing with only one set of the two, as far as real numbers are concerend there is no difference between them.

[taekahn]

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.

Your basic argument is flawed, stating that .999... is irrational to prove it is not equal to 1, a rational number. If in fact it is equal to 1, which is what we state, then .999.. must be rational.
This is the crux of the entire thread, the idea is to prove it, not restate it.

[Rock Monster]

they are not necesaily representing different REAL NUMBERS.

Ok... last post in this thread.... I promise.

Just because they REPRESENT the same real number, doesn't mean that they are equal. If the argument is if they are equal, no. If the argument is, do they represent the same number, then, I guess by your standards, yes.

[zdunklee]

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.

Your basic argument is flawed, stating that .999... is irrational to prove it is not equal to 1, a rational number. If in fact it is equal to 1, which is what we state, then .999.. must be rational.
This is the crux of the entire thread, the idea is to prove it, not restate it.

Exactly, there are hundreds of mathematically sound proofs that 0.999... and 1 are equal when dealing with real numbers, there are NONE that say they aren't.

[zdunklee]

they are not necesaily representing different REAL NUMBERS.

Ok... last post in this thread.... I promise.

Just because they REPRESENT the same real number, doesn't mean that they are equal. If the argument is if they are equal, no. If the argument is, do they represent the same number, then, I guess by your standards, yes.

Yes but according to the very DEFINITON of real numbers, two numbers are equal if the LIMIT of the two numbers as the go to infinity is equal.

The Limit of 0.9999... =1 as does the limit of 1. Thus by definiton they are equal.

[Queenie]

You motherEffers are giving me a horrible headache.

<<note to self: stay the Eff out of this thread

[zdunklee]

You're welcome Queenie.

[Philly Mike]

[quote="taekahn"]Mike, if you subtract .111

[taekahn]

You are the one on smack, break out PnP and do this.
1 - 1/9
Don't leave the answer as a fraction, carry out the division.
I can have victor help you if you need.

[zdunklee]

[quote="Philly Mike"]
[quote="taekahn"]Mike, if you subtract .111

[uhohspagettio]

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.

I agree with Allison on this and not because she is the hottest chick on the board, here is my example. When I want to order something at McDonalds I will say something along these lines, "I would like the #1 Value meal with a Coke." I do not say "I would like the #.999 Value meal with a Coke."

[Philly Mike]

first off it makes no sense to get .888... from subtracting .111...

and as far as god telling you so. god doesn't exist so lay of the LSD my friend.

Mike he is right, try it on your calculator just like adding .1111... to .9999.... gives you 1.1111...., If you subtract .1111.... from 1, you get .8888...

the whole thing is that the infinate numbers are represented by the closest relavant number. when you use a fraction it is a representation of the number without the infinite. therefore the infinates aren't really what you are calculating when you use the fractions.

and as far as the calculator work goes, that only counts for as many as you can put on the calculator and not the actual infinite, you can't really calculate an infinite with a calculator.

[zdunklee]

A fraction is the purest from of an infinite number 1/9 is treated as an infinite number in the calculator, 0.1111 might not be but 1/9 is.

Edit: 1/9 is the true form of 0.1111..., It is a rational number, just as any number that can be represented by a fraction is a rational number. Irrational numbers are those numbers that cannot be represented by fractions, such as SQRT(2),PI, e, and the natural logrithim.

[zdunklee]

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.

I agree with Allison on this and not because she is the hottest chick on the board, here is my example. When I want to order something at McDonalds I will say something along these lines, "I would like the #1 Value meal with a Coke." I do not say "I would like the #.999 Value meal with a Coke."

^so what, that doesn't have anything to do with it, 1 is easier to say, just like 1/2 is the preferred representation of 256/512.

[cuppie]

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

Just to let you know "Money is the root of all evil" is a misquote. It is actually, "For the love of money is the root of all evil" 1 Timothy 6:10

[zdunklee]

Either way it proves what we all know is true!

[Queenie]

I know I said I wasn't coming back in here, but I just had to post this:

111,111,111 x 111,111,111 = 12,345,678,987,654,321

[zdunklee]

What the hell is that queenie?


edit: oh I am an idiot, I see it now, that's one I didn't know! :-X

[Philly Mike]

A fraction is the purest from of an infinite number 1/9 is treated as an infinite number in the calculator, 0.1111 might not be but 1/9 is.

Edit: 1/9 is the true form of 0.1111..., It is a rational number, just as any number that can be represented by a fraction is a rational number. Irrational numbers are those numbers that cannot be represented by fractions, such as SQRT(2),PI, e, and the natural logrithim.

how is a fraction the truest form of a number???? that really makes no sense. A fraction is a representation of the division of the number. like 1/4 =.25 since the / denotes division so that would be saying 1

[Torque]

We need to get Zane to try and read this thread on air. His head will explode at the first proof.

[dingdongyo]

how is a fraction the truest form of a number???? that really makes no sense. A fraction is a representation of the--

MIKE, mike, mike, mike... mike....

you're being glib!

i think the meaning of "fraction is the truest form of a number" is that fractions are the simplest way to write out a representation of an irrational number. no matter how many decimal points you use, you can't write out the exact decimal of, oh, say 1/7.

"but you just said 0.999... = 1! how can you say that, and then tell me that using decimals for irrational numbers is inaccurate?"

we're using the "..." to represent an infinite repeat without wasting an assload of space.
1/7 = 0.142857...
...i think that works. which is truer? well, they are both true. take your pick. 1/7 is just easier.

keep an open mind here. the proof that 0.999... = 1 has been put in front of you several times already. if you can't understand it, it doesn't mean it's wrong.

[Torque]

+1 despite the fact that I had to see Tom Cruise

[Philly Mike]

how is a fraction the truest form of a number???? that really makes no sense. A fraction is a representation of the--

MIKE, mike, mike, mike... mike....

you're being glib!

i think the meaning of "fraction is the truest form of a number" is that fractions are the simplest way to write out a representation of an irrational number. no matter how many decimal points you use, you can't write out the exact decimal of, oh, say 1/7.

"but you just said 0.999... = 1! how can you say that, and then tell me that using decimals for irrational numbers is inaccurate?"

we're using the "..." to represent an infinite repeat without wasting an assload of space.
1/7 = 0.142857...
...i think that works. which is truer? well, they are both true. take your pick. 1/7 is just easier.

keep an open mind here. the proof that 0.999... = 1 has been put in front of you several times already. if you can't understand it, it doesn't mean it's wrong.

the reason you use a fraction to represent an infinite is because an infinite can't really be shown. A fraction is a definite number as best it can be shown the the decimal is an answer. the fraction is the simplest way to write it because it is the question that leads to the answer representing the answer as closely it can be rounded. since .999... can't be shown completely it is represented as the fraction that most closely represents it. Which is why they say it = 1 because 1 most closely represents .999... but it isn't the same number.

We need to get Zane to try and read this thread on air. His head will explode at the first proof.

and yes it would be fun hearing zane contemplating this one on the air.

[taekahn]

fractions are the simplest way to write out a representation of an irrational number.

I would take this one step further, fractions are often the simplest and most visually pleasing way to write out decimals. I don't recall walking into a department store and seeing a tag that says 0.50 off, they usually say 1/2 off. Yet, 0.50 easily fits and has the exact same meaning. This kind of deflates your most recent post mike, that "the reason [we] use a fraction to represent an infinite is because an infinite can't really be shown."

[speedbump]

I don't understand how this has gone on for 3 pages. You may THINK .999...=!1, but it doesn't matter, because people who have taken more math classes than you have proved you wrong.

[zdunklee]

A fraction is the purest from of an infinite number 1/9 is treated as an infinite number in the calculator, 0.1111 might not be but 1/9 is.

Edit: 1/9 is the true form of 0.1111..., It is a rational number, just as any number that can be represented by a fraction is a rational number. Irrational numbers are those numbers that cannot be represented by fractions, such as SQRT(2),PI, e, and the natural logrithim.

how is a fraction the truest form of a number???? that really makes no sense. A fraction is a representation of the division of the number. like 1/4 =.25 since the / denotes division so that would be saying 1

[taekahn]

So, what is next mike? Nullity or Zero as a number?

[Philly Mike]

I don't understand how this has gone on for 3 pages. You may THINK .999...=!1, but it doesn't matter, because people who have taken more math classes than you have proved you wrong.

actually it really doesn't matter to me, for a few reasons, 1 I don't care what mathematicians or math majors have to say unless it has an actual application. .999... = 1 has no bearing, and i still don't believe it is true. Even if i were to go with this what would it matter?

as far as the you never see .50 off in stores. Well you could have fooled me because they say 50% off which is .50 just with a % on one end instead of the . on the other. I have never seen them say "3/4 off in this insane offer" usually it is 75% off.

I was saying fractions were simpler anyway, so that has no bearing.

and tae, as far as nullility goes, well you and lee here can probably have a brain-dead conversation about that. .999... = 1 i can at least see why people believe it, but stating that 0 actually has value, well that is just plain retarded work that only a minger of high caliber could ever create.

[zdunklee]

I don't understand how this has gone on for 3 pages. You may THINK .999...=!1, but it doesn't matter, because people who have taken more math classes than you have proved you wrong.

actually it really doesn't matter to me, for a few reasons, 1 I don't care what mathematicians or math majors have to say unless it has an actual application. .999... = 1 has no bearing, and i still don't believe it is true. Even if i were to go with this what would it matter?

as far as the you never see .50 off in stores. Well you could have fooled me because they say 50% off which is .50 just with a % on one end instead of the . on the other. I have never seen them say "3/4 off in this insane offer" usually it is 75% off.

I was saying fractions were simpler anyway, so that has no bearing.

and tae, as far as nullility goes, well you and lee here can probably have a brain-dead conversation about that. .999... = 1 i can at least see why people believe it, but stating that 0 actually has value, well that is just plain retarded work that only a minger of high caliber could ever create.

They believe 0.999... = 1 only because that is how the real numbers have been defined, thus if you are talking about the real number system the two values are always equal. However there are number systems out there in which 0.999... =! 1, such as the p-adic numbers, but that would be a different topic altogether.

This is much the same idea that there is Euclidean Geometry(which is the geometry that everyone recognizes) and Spherical Geometry in which nothing is ever parallel and there are no lines.

If you really want to get into some crazy math discussion, how about we talk about the fact that all math done from the 19th century on was based upon the work of someone who never existed? ???

[Allyson]

I was tutoring a boy yesterday and I tried to tell him about imaginary numbers. He told me all numbers are imaginary. What is x? That is a letter in the alphabet.

This might take a while...