Does 2/6 Equal 1/3?

[Josh.Defibaugh]

i believe that its purely a mind matter. to all you mathematicians, its 2/6. but you regular folk, its 1/3

[iangb]

It took me a good five minutes to work that out, Suki. You properly nerd sniped me.

Solution

There's an extra assumption. a and b are real numbers, but they must also be different numbers, otherwise you multiply by 0 in the second line (multiply both sides by (a-b), which =0 if a=b). This means that when you get to the 'either/or' choice at the end, you cannot choose the one that leads to 'a=b' because that goes against your rules when choosing a and b.

[DemonzLunchBreak]

*is embarrassed*

I have an excuse for saying that, but that excuse is also embarrassing.

[Qwubble]

Philosopher point of view: (uses the pizza thing from before)

Mathematical point of view: yes, 1/3=2/6

My brother's point of view: well, if you went back in time and only cut the pizza into 3 parts instead of 6, and gave him one, he would still have the same amount. (basically the mathematical POV, he wanted me to post his point on it, cmon...hes 9)

Idiot point of view= NO!!! 1 and 3 aren't the same as 2 and 6


it really is a theoretical questions

(hey, this was to degrade into unintelligence some time, why not now?) :D

[t̷s͢uk̕a͡t͜ư]

It took me a good five minutes to work that out, Suki. You properly nerd sniped me.

Solution

There's an extra assumption. a and b are real numbers, but they must also be different numbers, otherwise you multiply by 0 in the second line (multiply both sides by (a-b), which =0 if a=b). This means that when you get to the 'either/or' choice at the end, you cannot choose the one that leads to 'a=b' because that goes against your rules when choosing a and b.

That's an awful wishy-washy way of putting it. Can't say that's unexpected coming from a Brit -- when you want the job done and done right good, you get a 'Merican.

It sets two solutions equal to each other.
It's wrong for the same reason the following is wrong:
9 = 9
(3)^2 = (-3)^2
3 = -3

[Destiny]

1/3 = 0.333333 recurring
2/6 = o.333333 recurring.

Problem solved

[Nexx]

It sets two solutions equal to each other.
It's wrong for the same reason the following is wrong:
9 = 9
(3)^2 = (-3)^2
3 = -3

I have to admit that proof thoroughly puzzled me. Even though I figured out what the problem was, I can't quite explain why it's wrong. Your explanation solves the problem, but is that really true?

If you've got x^2 = y^2 and you know nothing else about x and y, then your above solution would suggest that nothing can be said about x and y directly. But that's not true, is it? Can't we go a bit further and say that either x = y or x = -y? Then, as iangb implied, we would try 2 different cases: a = b and a != b. a = b would yield two trivial results (a+b=t and a=b), and a != b would yield a trivial result (a+b=t) and a wrong result (a=b, wrong because it contradicts an assumption). I'm not entirely sure that my initial step relating x and y covers all cases, though. Would you mind elaborating on your explanation?

[otters]

Yes, we need more unnecessary, mathematically invalid answers to this question. Thank you.

[DemonzLunchBreak]

Avarin:
x^2 = y^2
|x|=|y|

...And I still can't get over how unbelievably retarded my post was. u_u;;

[TheRealOne]

Yes, we need more unnecessary, mathematically invalid answers to this question. Thank you.

Well if that is what you want except for the invalid part. here you go.

i^(-i)=sqrt(e^(pi))

An imaginary number raised to the opposite of its self is equal to the square root of a transcendental number raised to another transcendental number. Crazy huh?

If anyone wants to post the proof using Eulers work.

*note* this has no baring to what incluye said, or to the discussion at hand. But to make it relevant I propose that since imaginary numbers can equal real numbers 2/6 has to equal 1/3.

[Qwubble]

I'm going to attack the Pizza story now, (I thought about this in math class today).

This time, you cut the pizza into 3 parts, and you get 1 of the pieces. But you would rather have smaller pieces so you cut the pizza into 6 pieces, and take 2. You have the same amount of pizza.

Here's the problem with the pizza thing though, the inability to put the pizza back together adds a variable to the whole problem, so really...it's an invalid argument.

[TheRealOne]

Here's the problem with the pizza thing though, the inability to put the pizza back together adds a variable to the whole problem, so really...it's an invalid argument.

And therein lies the paradox that allows blizz to troll now 6 pages.

[otters]

Yes, we need more unnecessary, mathematically invalid answers to this question. Thank you.

I...I think I might have been reading the wrong page.
Sorry for any misunderstanding.