Let's Prove It!

A good argument is hard to find. So when a friend told me his theory about the answer to the "Is the Glass Half

Full of Half Empty?" puzzle, I had to snatch it up. Here we discover the truth of optimism... it also makes a great

title.

Full of Half Empty?" puzzle, I had to snatch it up. Here we discover the truth of optimism... it also makes a great

title.

used to represent the dichotomy that is

pessimism and optimism? Imagine this scene

many moons ago: a man is sitting at his table and

his cup is before him. His wife fills his cup with

drink and they sit to eat their dinner. As time

passes, he sees his cup is not as full and thinks

"My cup should always be full." and tells his

wife to pour him some more. She tells him to

finish that wine first. He replies "In my universe,

my cups are not allowed to be half empty. It

must be filled." To which she replies "Well this

universe does not have the funds to support

your universe. Here, any wine in your cup is a

blessing so it is half full. Now eat your dinner"

According to the Merriam-Webster Dictionary, a glass is "2; something made of glass; esp: tumbler" A tumbler is "2: a drinking glass without foot or stem."

These definitions do not make mention of anything occupying the space of a glass so we can say that a glass has a volume that is intrinsically empty. Thus,

we can state the universal statement that "all drinking glasses are intrinsically empty."

When we say "Is the glass half full or half empty" we are really asking if the volume of the glass is occupied by stuff and is it equal to "a half", and if so, was

it subtracted or added from the properties of the glass?

To do this, let's say that the volume occupied by the glass is*V* (the empty set) which is a subset of the universe of the glass, say universe *G*. We then see if

the element, say* k*, does not exist in* V* (the empty set or "the glass is empty") or does exist in* V* (there is a volume occupied by stuff). If the element* k* exists

in* V*, we then see if* k* is equal to "a half' such that "a half" is a predetermined element of some other universe.

If these condition are met, we can then see if*k *was added or subtracted from the properties of the *glass*.

Since the glass is by definition empty, any solid, liquid, gas or stuff in the plasma state, is in a**conjunction** to the properties of the glass and is an **addition**.

Therefore, since the definition of a glass, as stated above, means the glass is empty, any element*k* that exists in *V* must be an element of another set that is in

conjunction with*V*. Hence, the properties of a glass do not allow for anything but *V* to be empty and thus anything occupying space in *V* is an addition.

Thus, the glass is always considered "half full".

:::JDS:::

Let the truth of optimism prevail!

These definitions do not make mention of anything occupying the space of a glass so we can say that a glass has a volume that is intrinsically empty. Thus,

we can state the universal statement that "all drinking glasses are intrinsically empty."

When we say "Is the glass half full or half empty" we are really asking if the volume of the glass is occupied by stuff and is it equal to "a half", and if so, was

it subtracted or added from the properties of the glass?

To do this, let's say that the volume occupied by the glass is

the element, say

in

If these condition are met, we can then see if

Since the glass is by definition empty, any solid, liquid, gas or stuff in the plasma state, is in a

Therefore, since the definition of a glass, as stated above, means the glass is empty, any element

conjunction with

Thus, the glass is always considered "half full".

:::JDS:::

Let the truth of optimism prevail!

Bibliography

The Merriam-Webster Dictionary, 1997

The Merriam-Webster Dictionary, 1997

Suggested Reading

*Symbolic Logic* 5th ed. Irving Copi. Prentice Hall. 1979

*How to Prove It* Daniel Velleman. Cambridge. 1994

*Elementary Analysis: The Theory of Calculus *Kennith A Ross. Springer. 2000

*How to Read and Do Proofs* Daniel Solow. Wiley. 1982

*The Iliad* Homer. Long time ago.

Let me just say that this is a great argument when the universe is for the glass and its subset of volume. Maybe if we look at it semantically, the meaning is different.

Perhaps this phrase best makes sense when looked at with the perspective of the element occupying the volume. By removing the volume and making that the universe, we

can say that the volume cannot be the empty set because then it would not exist (as a volume) and thus must contain the element*k*. Since this element may be equal to "a

half" we can see if this element is added or subtracted to the properties of the volume itself. This would prove difficult since the element would be the volume and since it

is the volume, it cannot be a half of itself. We would need another universe and that is not something I feel like doing.

Perhaps this phrase best makes sense when looked at with the perspective of the element occupying the volume. By removing the volume and making that the universe, we

can say that the volume cannot be the empty set because then it would not exist (as a volume) and thus must contain the element

half" we can see if this element is added or subtracted to the properties of the volume itself. This would prove difficult since the element would be the volume and since it

is the volume, it cannot be a half of itself. We would need another universe and that is not something I feel like doing.