Beer Theorem 1.
An infinite crowd of mathematicians enters a bar.
The first one orders a pint, the second one a half pint, the third one a quarter pint…
“Got it”, says the bartender – and pours two pints.
Proof.
Let .
Then
.
Therefore,
.
When ,
i.e.,
.
There is also a proof without words at all:
Beer Theorem 2.
An infinite crowd of mathematicians enters a bar.
The first one orders a pint, the second one a half pint, the third one a third of pint…
“Get out here! Are you trying to ruin me?”, bellows the bartender.
Proof.