A Full Glass = A Empty Glass, what is wrong in the proof?

Question

We know that
A glass filled up to half it's height = A half full glass ---(1)

We also know that
A glass filled up to half it's height = A half empty glass ---(2)

Comparing equations (1) and (2), since the Left hand side of both equations are same, so we can say that right hand sides of both equations will be same, i.e.

A half full glass = A half empty glass ---(3)

Multiplying equation (3) by 2 on both sides, we have
2 x half full glass = 2 x half empty glass ---(4)

Alternatively equation (4) can be written as
A full glass = A Empty glass

What is wrong in above proof?

Answer 1

Hmmm... This is called transitive property. Heard of it? It means that if a=b and a=c, then b=c because b and c equal to a. Same apply to the glasses. If half full equals full and half full equals empty, then full equals empty. Get it? PM me in my info page if you still have question.

Answer 2

A glass filled up to half it's height is not equal to half an empty glass because half an empty glass is 0 only as 0/2=0 and not 1/2

Answer 3

You are assuming the following:
2 x half full glasses = a full glass
2 x half empty glasses = an empty glass

If we take the standard convention that 2a = a+a then the second assumption that 2 half empty glasses add up to an empty glass would be wrong.

Answer 4

Multiplying equation (3) by 2 on both sides, we have
2 x half full glass = 2 x half empty glass ---(4)

you can't multiply two equations like that

Answer 5

Last line should be
Full glass + Empty Glass= Empty glass + Full Glass

Remember each side of the equation has two glasses and enough water to fill one glass full of water (or two glasses half full)

Answer 6

When u say 2 x half full glass........u can't change it to ONE FULL GLASS......
It can be changed to 2 half full glasses.......
And the other to 2 half empty glasses........
Then u can see that they are the same....or comparable....!!!!
I think this is what is wrong in this proof......!

Answer 7

well its not a mathematical theory its trying to prove here...the main purpose of this is to see how people view situations or just life in general in regards to a pessimistic attitude or an optimistic attitude.

your proof is wrong see you the thing is you have a 1/2 on both sides regardless of of the point of view
1/2=1/2
2*1/2=2*1/2
1=1
so the cup is always filled with the same amount, the perception of it is what changes...

Answer 8

Hi. One deals with a positive value, one deals with a negative value.

Answer 9

its just the way your perspective is i se the glass as to wide :P