Does 2/6 Equal 1/3?

[Kablizzy]

I posit that it does not. 1/3 does not equal 2/6. Discuss.

[Condog]

I say yes.

1 x 2 = 2
3 x 2 = 6

1 x 2 = 2
3 x 2 = 6

∴ 1/3 = 2/6

[BNW]

You can take two sides to this.

Is this purely mathematical or is it used as a real world example?

Mathematically it is obvious that 2/6 = 1/3.

I could pose a real world example that would differ. (Remember the only mathematics I am using here is the fact that there are numbers and fractions, nothing more, nothing less.)

Let us say you have a pizza. It is sliced into 6 pieces. Joe takes 2 pieces. Your mind thinks he has 1/3 of the pizza, but that is purely mathematical theory. In fact he has 2/6 of the pizza. He didn't morph the pizza back together and form 3 pieces. There are still 6 pieces. So in this example 1/3 does not = 2/6. You can't morph 2 pieces of pizza into 1.

[rambo5252]

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

[Condog]

Let us say you have a pizza. It is sliced into 6 pieces. Joe takes 2 pieces. Your mind thinks he has 1/3 of the pizza, but that is purely mathematical theory. In fact he has 2/6 of the pizza. He didn't morph the pizza back together and form 3 pieces. There are still 6 pieces. So in this example 1/3 does not = 2/6. You can't morph 2 pieces of pizza into 1.

Yes, but relating back to the mathematical side, those two pieces are still equal in area to 1/3 of the pizza.

@rambo :: Don't flame, this is Debate. Keep your posts coherent and relative.

@Kablizzy :: What evidence do you have to support your claim? You haven't given me anything to counter in order to prove/disprove your argument.

[Lightning55]

2/6 does not equal 1/3

In theory it does but 2/2(1/3)=2/6

Technically 2/2 is still 1. 1 is a number that affects the outcome of 1/3 time the number. Therefore, neither 1/3 or 2/6 = 1/3.

[乳头的早餐谷物]

2/6 certainly doesn't look like 1/3. I agree with Kablizzy.

Especially if that six is actually an upside-down nine—and who are we to say it isn't?

[DemonzLunchBreak]

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

Read the forum guidelines, please. And then follow them.

[Izzy]

It doesn't. For one reason:

Kablizzy said so.

There, proven.

[BNW]

It doesn't. For one reason:

Kablizzy said so.

There, proven.

I think it is funny how when I put a math joke and sarcastic comment in here that I get called a retard.

I agree whole heartedly with Izzy on this. Blizz is right.

[Condog]

It doesn't. For one reason:

Kablizzy said so.

There, proven.

I think it is funny how when I put a math joke and sarcastic comment in here that I get called a retard.

I agree whole heartedly with Izzy on this. Blizz is right.

I find it funny how you will blindly follow Kablizzy on this simply because he is who he is. He has no evidence argument beyond "I posit that it does not. 1/3 does not equal 2/6", and no evidence to support that hypothesis. At least wait for Blizz to provide some semblance of reasoning before you go jumping on the bandwagon.

[otters]

The Multiplicative Identity Axiom states that multiplying a number by 1 does not change the number. Remeber, this is an axiom, so it is accepted without proof.

1 x 2 = 2
3 x 2 = 6

2 = 1
2 = 1, and since 1/1 = 1 this follows the axiom.

Touché.

[Atilla]

I'm pretty sure the second of June doesn't equal the first of March. Or is it the sixth of February and the third of January? Either way, totally different days.

[DemonzLunchBreak]

Haha, Atilla.

Is this just a parody of that one time when a huge debate erupted over 1 and .(9)?

[Qix]

I'm pretty sure the second of June doesn't equal the first of March. Totally different days.

Not on my watch.

[capt_weasle]

Shootdangit don't you people ever know your Asch?

I don't give a crap everyone says it's line B, CRAPWAFFLE IT IS STILL LINE C.

[Condog]

Here is my argument. Nice coloured pictures for you all.

@incluye :: You call that a touché? This is a touché.

[JetPack]

In mathmatical terms, 2/6 does equal 1/3. 2 dived by 6 is .33333 etc and the same goes for 1 divided by 3. Try it in a calculator if you don't believe me.
In real terms, 2/6 and 1/3 would not always look the same, but they would equal the same amount.

[fingersonthefrets]

2/6 = 2/9 following maestro's logic that is obviously correct.

therefore 2/6 = 0.2222222222222222...222..22..... .. ..2 ..
and we've worked out that 1/3 = 0.333333333333

so they are obviously very different

you obviously have 2/9 of a brain corny.

[yungerkid]

define equals. they are not exactly the same, but they are quantitatively the same quantity.

[scythe]

Last I checked, playing track 2 of 6 wasn't the same as playing track 1 of 3. I don't see how those can be considered equal.

[t̷s͢uk̕a͡t͜ư]

You're using mathematical symbols and terminology, so I'll assume you're asking us to do this within the realm of mathematics, which entails accepting all of the axioms mathematics relies upon to remain consistent and functional. If you don't mind, I'll also assume you're cool with fundamentals like the definition of one, miscellaneous properties and definitions of basic operators, etc.

According to extensions of the axioms you must accept in order to be talking about the same mathematics that I am, two-sixths can be shown to be equal to one-third in a number of ways.
Here's one:
In the one-dimensional vector space, the multiplicative identity is 1. This means, from the definition of the multiplicative identity, that performing a vector multiplication as defined by the vector space of any vector in the vector space with the multiplicative identity will not change the value of the vector being multiplied by the multiplicative identity.
According to the definition of division in the one-dimensional vector space, any vector (that is not the zero vector as defined by the containing vector space) divided by itself is equal to the multiplicative identity.
If I can find some way to change either of one-third or two-sixths so that it becomes exactly the same expression as the other, and do so using only operations that do not change its value, then the two expressions are equal.
If I take one-third and multiply it with the multiplicative identity, then its value will not change. Call it random or brilliant intuition, but I have this crazy feeling that the multiplicative identity in the form of two-halves will be useful for this case. If I apply the definition of multiplication between the fractions one-third and two-halves, I get the fraction two-sixths, and the value has not changed according to the definition of the multiplicative identity. I have succeeded in performing the task I have described; I have demonstrated, under the definitions extrapolated from the axioms declared by mathematics, that one-third is equal to two-sixths.

I have just given you compelling reason to believe that 2/6 = 1/3. I can also demonstrate that this remains true in practice.
If you're saying that you're not convinced (which doesn't appear to be the case), then you can step up and challenge any part of this reasoning or you can keep your ignorance to yourself. But you can't assert it's false unless you can attack the reasoning, find an inconsistency, or assert and support an assertion that entails that this is false.
But in this case, it looks like you're asserting that this is false. If you still think this, you need to show a flaw in reasoning or an inconsistency, and furthermore provide supporting arguments in favor of your assertion, if you want to convince anyone or are interested in not being a dumby-dumbhead.


tl;dr:
2/6 = (1*2)/(3*2) = (1*2)/(3*2) = 1/3 --> lolwut

[BNW]

You're using mathematical symbols and terminology, so I'll assume you're asking us to do this within the realm of mathematics, which entails accepting all of the axioms mathematics relies upon to remain consistent and functional. If you don't mind, I'll also assume you're cool with fundamentals like the definition of one, miscellaneous properties and definitions of basic operators, etc.

According to extensions of the axioms you must accept in order to be talking about the same mathematics that I am, two-sixths can be shown to be equal to one-third in a number of ways.
Here's one:
In the one-dimensional vector space, the multiplicative identity is 1. This means, from the definition of the multiplicative identity, that performing a vector multiplication as defined by the vector space of any vector in the vector space with the multiplicative identity will not change the value of the vector being multiplied by the multiplicative identity.
According to the definition of division in the one-dimensional vector space, any vector (that is not the zero vector as defined by the containing vector space) divided by itself is equal to the multiplicative identity.
If I can find some way to change either of one-third or two-sixths so that it becomes exactly the same expression as the other, and do so using only operations that do not change its value, then the two expressions are equal.
If I take one-third and multiply it with the multiplicative identity, then its value will not change. Call it random or brilliant intuition, but I have this crazy feeling that the multiplicative identity in the form of two-halves will be useful for this case. If I apply the definition of multiplication between the fractions one-third and two-halves, I get the fraction two-sixths, and the value has not changed according to the definition of the multiplicative identity. I have succeeded in performing the task I have described; I have demonstrated, under the definitions extrapolated from the axioms declared by mathematics, that one-third is equal to two-sixths.

I have just given you compelling reason to believe that 2/6 = 1/3. I can also demonstrate that this remains true in practice.
If you're saying that you're not convinced (which doesn't appear to be the case), then you can step up and challenge any part of this reasoning or you can keep your ignorance to yourself. But you can't assert it's false unless you can attack the reasoning, find an inconsistency, or assert and support an assertion that entails that this is false.
But in this case, it looks like you're asserting that this is false. If you still think this, you need to show a flaw in reasoning or an inconsistency, and furthermore provide supporting arguments in favor of your assertion, if you want to convince anyone or are interested in not being a dumby-dumbhead.


tl;dr:
2/6 = (1*2)/(3*2) = (1*2)/(3*2) = 1/3 --> lolwut

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

[origami_alligator]

Last I checked, playing track 2 of 6 wasn't the same as playing track 1 of 3. I don't see how those can be considered equal.

Assuming the two records in question are the same artist, just one album has been split into 6 equal parts (to protect the copyright of course), and the other is the complete 3 songs.
Playing track 1 of the 3 song album is normal, but playing track 2 of the 6 song album yields either (a) the very ending moments of the previous song only, (b) the ending of the previous song and the beginning of the next song, (c) the very beginning of the next song, (d) somewhere after the beginning of the second song, or (e) does the same as above except with songs 2 and 3 instead of songs 1 and 2.
This yields a very different musical experience. Suggesting that each track of the 3 song album is exactly the same length throughout means that track 2 on the 6 song album is only the last half of the 1st song on the 3 song album.

If you're playing from 0/6 to the end of 2/6 of the album then you get 1 whole song, and your experience hasn't changed. It's all subjective, fools.

[//Zander]

so I'm just gunna ignore all that lots of writing and say that:
1/3 is said as one third and if you have a pizza and eat 4 of the six peices you get 2/6 pieces of pizza. but you have on third of the pizza you had so it is the same friggin thing...