**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.*