Does 2/6 Equal 1/3?

[Condog]

Well, what DOES the big bad wolf population eat these days? Corn?

GW would never eat me! Take it back!

[T3chno]

Well, what DOES the big bad wolf population eat these days? Corn?

You have to note, Kablizzy is quickly removing the elk population. And we all know elks are the main source of food for these wolves.

[Atilla]

I think 1/3 will vote for McCain, 2/6 will vote for Obama, and the vast majority (3/9) will simply not vote.

If the majority refuses to vote, nobody should be elected, and the government should dissolve.

[blue_tetris]

I think 1/3 will vote for McCain, 2/6 will vote for Obama, and the vast majority (3/9) will simply not vote.

If the majority refuses to vote, nobody should be elected, and the government should dissolve.

I disagree. Just because most people don't have an opinion on who should run the government doesn't mean that those people must believe that they don't want a government. The people who don't vote are electing everyone else to decide.

[Atilla]

I think that if most people don't care who runs the country, we should respect that by adopting anarchy. Anything less would be denying the right of hard-workin', God-fearin' Americans to have their say. Or not have it, in the circumstances.

[blue_tetris]

I think that if most people don't care who runs the country, we should respect that by adopting anarchy. Anything less would be denying the right of hard-workin', God-fearin' Americans to have their say. Or not have it, in the circumstances.

Just because you don't want apples or oranges doesn't mean you necessarily want bananas. I'd rather have people not vote at all than vote for a candidate that they don't support.

If the candidates see "10% for A" and "11% for B", maybe next time they'll have to get better candidates to tap into that 79% who didn't think either candidate was worth voting for.

There are these bullshit ads that run saying "Get out there and vote! it doesn't matter who you vote for!" What?! I think, if you don't care who you vote for, you should probably withhold your vote. The election just might matter to someone else.

[29403]

It's the same thing.
Except there might be a different digit on one end of the infinite decimal of one of these fractions. We probably won't know.

[t̷s͢uk̕a͡t͜ư]

It's the same thing.
Except there might be a different digit on one end of the infinite decimal of one of these fractions. We probably won't know.

"End of the infinite" does not compute.

[blue_tetris]

"End of the infinite" makes sense for some infinite sets, like the set of all x where x < 2.

But for 29403's example, no, there's nothing that terminates a repeating digit decimal. It's only a repeating digit because of the decimal system that we're using to demonstrate the value--it has nothing to do with the quantity of the value itself.

[t̷s͢uk̕a͡t͜ư]

"End of the infinite" makes sense for some infinite sets, like the set of all x where x < 2.

It still doesn't, though. Let's say you're trying to find "the greatest number less than two." This is not a possible task, because any number you name, I can average with two and get one even closer. Even though we can express it as a limit, even, there is no "end" to the numbers as they get closer to two.

[jean-luc]

"End of the infinite" makes sense for some infinite sets, like the set of all x where x < 2.

It still doesn't, though. Let's say you're trying to find "the greatest number less than two." This is not a possible task, because any number you name, I can average with two and get one even closer. Even though we can express it as a limit, even, there is no "end" to the numbers as they get closer to two.

True.
I am assuming that you mean all real x.
Cantor's Diagonal Argument lets us prove that there are an infinite number of points.

Go ahead and write down every number between 0 and 2, to an infinite accuracy (we'll only look at the nonnegative reals < 2 right now for simplicity, but this works all reals < 2 as well.).
You've just written down every number, right?

Now, start with the number in the very top left hand corner, and going down diagonally. That is, the 1st digit of the 1st number, the 2nd digit of the 2nd number, the 3rd digit of the 3rd number, etc.
Take each digit, add one (looping to 0 if it's a 9), and write it down.

The number you just wrote down isn't in the original set. You can do this infinitely.

Cantor's Diagonal Argument, in the larger context of Set Theory, shows that the real numbers are uncountable - that is, it is not possible to assign a counting number (1, 2, 3, etc...) to every real number. The argument works nicely in this situation to prove the infinity of points between two given points.

[t̷s͢uk̕a͡t͜ư]

True.
I am assuming that you mean all real x.
Cantor's Diagonal Argument lets us prove that there are an infinite number of points.

Go ahead and write down every number between 0 and 2, to an infinite accuracy (we'll only look at the nonnegative reals < 2 right now for simplicity, but this works all reals < 2 as well.).
You've just written down every number, right?

Now, start with the number in the very top left hand corner, and going down diagonally. That is, the 1st digit of the 1st number, the 2nd digit of the 2nd number, the 3rd digit of the 3rd number, etc.
Take each digit, add one (looping to 0 if it's a 9), and write it down.

The number you just wrote down isn't in the original set. You can do this infinitely.

Cantor's Diagonal Argument, in the larger context of Set Theory, shows that the real numbers are uncountable - that is, it is not possible to assign a counting number (1, 2, 3, etc...) to every real number. The argument works nicely in this situation to prove the infinity of points between two given points.

Yep, I've seen that before. And it was interesting to see it again despite the fact that no one was contesting that there are an infinite number of real numbers. We were going on a tangent about whether it makes sense to talk about the "end" of the infinites, not challenging the idea that R^1 is an infinite set.

[bobaganuesh_2]

bnwn, your retarded he hasnt morphed the pizza but thers still 2/3s left and he has 1/3, this is stupid 1/3 always equals 2/6

I concur w/ BNW

[EdoI]

1 / 3 = 0.33
10
- 9
10
- 9


2 / 6 = 0.33
-20
18
20

In both of cases I can just go on forever and there's NO WAY that it will ever get changed because

3x3 will always be 9, 10-9 will always be 1 and we always have to add one zero

3x6 will always be 18, 20-18 will always be 2 and we always have to add one zero

[scythe]

"End of the infinite" makes sense for some infinite sets, like the set of all x where x < 2.

It still doesn't, though. Let's say you're trying to find "the greatest number less than two." This is not a possible task, because any number you name, I can average with two and get one even closer. Even though we can express it as a limit, even, there is no "end" to the numbers as they get closer to two.

True.
I am assuming that you mean all real x.
Cantor's Diagonal Argument lets us prove that there are an infinite number of points.

Go ahead and write down every number between 0 and 2, to an infinite accuracy (we'll only look at the nonnegative reals < 2 right now for simplicity, but this works all reals < 2 as well.).
You've just written down every number, right?

Now, start with the number in the very top left hand corner, and going down diagonally. That is, the 1st digit of the 1st number, the 2nd digit of the 2nd number, the 3rd digit of the 3rd number, etc.
Take each digit, add one (looping to 0 if it's a 9), and write it down.

The number you just wrote down isn't in the original set. You can do this infinitely.

Cantor's Diagonal Argument, in the larger context of Set Theory, shows that the real numbers are uncountable - that is, it is not possible to assign a counting number (1, 2, 3, etc...) to every real number. The argument works nicely in this situation to prove the infinity of points between two given points.

That's not a proper use of the diagonal argument.
Infinite is an entirely different concept than uncountable. Everything uncountable is infinite, but not everything infinite is uncountable. In the previous example, I could just as well limit it to rational numbers <2, which are countable, but there is still no largest rational number less than 2.
Neither of those makes Dave wrong, though, since there can be an end to a closed set; the set of all numbers less than or equal to 2, which does have a largest value: 2.

[blue_tetris]

I think, originally, I intended to say less than or equal to. The set of all real x where x < 2 ends. It ends where x would otherwise equal 2. It does not "go on to infinity".

The point was to prove that the phrase "end of the infinite" makes sense for certain infinite sets. It makes sense for the set of all real x, where x is less than or equal to a constant. That set of x is infinite and possesses an "end of the infinite". That was the point.

*ends up bewildered as to where this could go next*

[BNW]

I have no idea why you guys are using a diagonal argument when the question is whether 1/3 = 2/6.

There is no proof (that I know of) that disproves this statement.

I don't intend to dwell on the subject right now. I have bigger fish to fry (mainly resistance in mediums and certain ways of calculating time). So I'm not going to try and make one up.

For me 1/3 will always equal 2/6 by multiplication of the 1 identity of 2/2.

MEH!

[t̷s͢uk̕a͡t͜ư]

I think, originally, I intended to say less than or equal to. The set of all real x where x < 2 ends. It ends where x would otherwise equal 2. It does not "go on to infinity".

The point was to prove that the phrase "end of the infinite" makes sense for certain infinite sets. It makes sense for the set of all real x, where x is less than or equal to a constant. That set of x is infinite and possesses an "end of the infinite". That was the point.

*ends up bewildered as to where this could go next*

That wouldn't be an acceptable proof in any sense of the word (or mathematical conceptualization thereof) other than a loose, informal argument on its behalf.
All you've done is give an example case, which anyone who has done ever studied mathematical proofs can tell you does not prove a damned thing. I therefore decry your efforts at subverting the potential impressionable minds who visit these forums as psychological terrorism. I ask that you refrain from posting again in this thread so that you don't aggravate the matter any further.

That's why the nature of infinity is the way I have said it to be -- those who don't agree are terrorists and liars, and at least one of them hates both America and the Baby Jesus.

[BNW]

I think, originally, I intended to say less than or equal to. The set of all real x where x < 2 ends. It ends where x would otherwise equal 2. It does not "go on to infinity".

The point was to prove that the phrase "end of the infinite" makes sense for certain infinite sets. It makes sense for the set of all real x, where x is less than or equal to a constant. That set of x is infinite and possesses an "end of the infinite". That was the point.

*ends up bewildered as to where this could go next*

That wouldn't be an acceptable proof in any sense of the word (or mathematical conceptualization thereof) other than a loose, informal argument on its behalf.
All you've done is give an example case, which anyone who has done ever studied mathematical proofs can tell you does not prove a damned thing. I therefore decry your efforts at subverting the potential impressionable minds who visit these forums as psychological terrorism. I ask that you refrain from posting again in this thread so that you don't aggravate the matter any further.

That's why the nature of infinity is the way I have said it to be -- those who don't agree are terrorists and liars, and at least one of them hates both America and the Baby Jesus.

I seriously almost fell out of my chair at this. My former argument still holds with me. No proof exists, so MEH!

[bobaganuesh_2]

[long-ass rant]

I'm still following the same logic as scythe.

Out of a 3 song list and a 6 song list, playing the first and second respectively will yield the idea that you are playing the song one-third the way into the album. Yet, if I were to have two completely different albums, then there would be no resemblence.

I will stop with the bitchery now and quit with the sarcasm.

I can't support an argument for this without using the mathematical Identity.

MATH wins.

/end sarcasm

/continue loving and learning mathematics for fun. :D

ur original post said it all. Math is not the answer, merely a paradox.

[Sithmaster]

2/6 only equals 1/3 if you use math, but, because anything involving fractions is a part of math, than yes, 2/6 = 1/3

[ninja143]

all numbers are math there fore even when you use numbers it is considered math, even a phone number can be math so i agree that 1/3=2/6

now if your fraction was 1/3=2/16 i would have to say your full of something but i dont know what and you need to check your math.

[t̷s͢uk̕a͡t͜ư]

even a phone number can be math

*cocks eyebrow*

[乳头的早餐谷物]

even a phone number can be math

*cocks eyebrow*

I knew there was a deeper meaning to 867-5309.

[Skyling]

I knew there was a deeper meaning to 867-5309.

Yes, in fact. Hmm.



Well, apparently it's -4442. Who knew.